diff --git a/cpp/src/arrow/compute/kernels/chunked_internal.h b/cpp/src/arrow/compute/kernels/chunked_internal.h
index 69f439fccf0..89ddcbcab01 100644
--- a/cpp/src/arrow/compute/kernels/chunked_internal.h
+++ b/cpp/src/arrow/compute/kernels/chunked_internal.h
@@ -61,6 +61,19 @@ struct ResolvedChunk<Array> {
   bool IsNull() const { return array->IsNull(index); }
 };
 
+// ResolvedChunk specialization for StructArray
+template <>
+struct ResolvedChunk<StructArray> {
+  // The target structarray in chunked array.
+  const StructArray* array;
+  // The index in the target array.
+  const int64_t index;
+
+  ResolvedChunk(const StructArray* array, int64_t index) : array(array), index(index) {}
+
+  bool IsNull() const { return array->field(static_cast<int>(index)) == nullptr; }
+};
+
 struct ChunkedArrayResolver : protected ::arrow::internal::ChunkResolver {
   ChunkedArrayResolver(const ChunkedArrayResolver& other)
       : ::arrow::internal::ChunkResolver(other.chunks_), chunks_(other.chunks_) {}
diff --git a/cpp/src/arrow/compute/kernels/vector_array_sort.cc b/cpp/src/arrow/compute/kernels/vector_array_sort.cc
index 324a435441f..3d37b8f4942 100644
--- a/cpp/src/arrow/compute/kernels/vector_array_sort.cc
+++ b/cpp/src/arrow/compute/kernels/vector_array_sort.cc
@@ -173,6 +173,49 @@ class ArrayCompareSorter {
   }
 };
 
+template <typename ArrowType>
+class StructArrayCompareSorter {
+  using ArrayType = typename TypeTraits<ArrowType>::ArrayType;
+
+ public:
+  // `offset` is used when this is called on a chunk of a chunked array
+  NullPartitionResult operator()(uint64_t* indices_begin, uint64_t* indices_end,
+                                 const Array& array, int64_t offset,
+                                 const ArraySortOptions& options) {
+    const auto& values = checked_cast<const ArrayType&>(array);
+    nested_value_comparator_ = std::make_shared<NestedValuesComparator>();
+
+    if (nested_value_comparator_->Prepare(values) != Status::OK()) {
+      // TODO: Improve error handling
+      return NullPartitionResult();
+    }
+
+    const auto p = PartitionNulls<ArrayType, StablePartitioner>(
+        indices_begin, indices_end, values, offset, options.null_placement);
+
+    bool asc_order = options.order == SortOrder::Ascending;
+    std::stable_sort(p.non_nulls_begin, p.non_nulls_end,
+                     [&offset, &values, asc_order, this](uint64_t left, uint64_t right) {
+                       // is better to do values.fields.size() or
+                       // values.schema().num_fields() ?
+                       for (ArrayVector::size_type fieldidx = 0;
+                            fieldidx < values.fields().size(); ++fieldidx) {
+                         int result = nested_value_comparator_->Compare(
+                             values, fieldidx, offset, asc_order ? left : right,
+                             asc_order ? right : left);
+                         if (result == -1)
+                           return true;
+                         else if (result == 1)
+                           return false;
+                       }
+                       return false;
+                     });
+    return p;
+  }
+
+  std::shared_ptr<NestedValuesComparator> nested_value_comparator_;
+};
+
 template <typename ArrowType>
 class ArrayCountSorter {
   using ArrayType = typename TypeTraits<ArrowType>::ArrayType;
@@ -409,6 +452,11 @@ struct ArraySorter<
   ArrayCompareSorter<Type> impl;
 };
 
+template <typename Type>
+struct ArraySorter<Type, enable_if_t<is_struct_type<Type>::value>> {
+  StructArrayCompareSorter<Type> impl;
+};
+
 struct ArraySorterFactory {
   ArraySortFunc sorter;
 
@@ -507,6 +555,13 @@ void AddArraySortingKernels(VectorKernel base, VectorFunction* func) {
   DCHECK_OK(func->AddKernel(base));
 }
 
+template <template <typename...> class ExecTemplate>
+void AddArraySortingNestedKernels(VectorKernel base, VectorFunction* func) {
+  base.signature = KernelSignature::Make({Type::STRUCT}, uint64());
+  base.exec = ExecTemplate<UInt64Type, StructType>::Exec;
+  DCHECK_OK(func->AddKernel(base));
+}
+
 const ArraySortOptions* GetDefaultArraySortOptions() {
   static const auto kDefaultArraySortOptions = ArraySortOptions::Defaults();
   return &kDefaultArraySortOptions;
@@ -561,6 +616,7 @@ void RegisterVectorArraySort(FunctionRegistry* registry) {
   base.init = ArraySortIndicesState::Init;
   base.exec_chunked = ArraySortIndicesChunked;
   AddArraySortingKernels<ArraySortIndices>(base, array_sort_indices.get());
+  AddArraySortingNestedKernels<ArraySortIndices>(base, array_sort_indices.get());
   DCHECK_OK(registry->AddFunction(std::move(array_sort_indices)));
 
   // partition_nth_indices has a parameter so needs its init function
diff --git a/cpp/src/arrow/compute/kernels/vector_sort.cc b/cpp/src/arrow/compute/kernels/vector_sort.cc
index 94c80b9f80d..261691bc57a 100644
--- a/cpp/src/arrow/compute/kernels/vector_sort.cc
+++ b/cpp/src/arrow/compute/kernels/vector_sort.cc
@@ -188,6 +188,8 @@ class ChunkedArraySorter : public TypeVisitor {
     return Status::OK();
   }
 
+  Status Visit(const StructType&) override { return SortInternal<StructType>(); }
+
  private:
   template <typename Type>
   Status SortInternal() {
@@ -269,25 +271,18 @@ class ChunkedArraySorter : public TypeVisitor {
   template <typename ArrayType>
   void MergeNonNulls(uint64_t* range_begin, uint64_t* range_middle, uint64_t* range_end,
                      const std::vector<const Array*>& arrays, uint64_t* temp_indices) {
-    const ChunkedArrayResolver left_resolver(arrays);
-    const ChunkedArrayResolver right_resolver(arrays);
+    const ChunkedArrayResolver chunk_resolver(arrays);
+    ResolvedChunkComparator<ArrayType> resolved_chunk_comparator;
 
     if (order_ == SortOrder::Ascending) {
       std::merge(range_begin, range_middle, range_middle, range_end, temp_indices,
                  [&](uint64_t left, uint64_t right) {
-                   const auto chunk_left = left_resolver.Resolve<ArrayType>(left);
-                   const auto chunk_right = right_resolver.Resolve<ArrayType>(right);
-                   return chunk_left.Value() < chunk_right.Value();
+                   return resolved_chunk_comparator.Compare(chunk_resolver, left, right);
                  });
     } else {
       std::merge(range_begin, range_middle, range_middle, range_end, temp_indices,
                  [&](uint64_t left, uint64_t right) {
-                   const auto chunk_left = left_resolver.Resolve<ArrayType>(left);
-                   const auto chunk_right = right_resolver.Resolve<ArrayType>(right);
-                   // We don't use 'left > right' here to reduce required
-                   // operator. If we use 'right < left' here, '<' is only
-                   // required.
-                   return chunk_right.Value() < chunk_left.Value();
+                   return resolved_chunk_comparator.Compare(chunk_resolver, right, left);
                  });
     }
     // Copy back temp area into main buffer
diff --git a/cpp/src/arrow/compute/kernels/vector_sort_internal.h b/cpp/src/arrow/compute/kernels/vector_sort_internal.h
index d8b024525c8..bd58b9483ea 100644
--- a/cpp/src/arrow/compute/kernels/vector_sort_internal.h
+++ b/cpp/src/arrow/compute/kernels/vector_sort_internal.h
@@ -456,6 +456,149 @@ Status SortChunkedArray(ExecContext* ctx, uint64_t* indices_begin, uint64_t* ind
                         const ChunkedArray& values, SortOrder sort_order,
                         NullPlacement null_placement);
 
+class NestedValuesComparator {
+ public:
+  // StructArray Compare overload
+  int Compare(StructArray const& array, uint64_t field_index, uint64_t offset,
+              uint64_t leftrowidx, uint64_t rightrowidx) {
+    std::shared_ptr<Array> field = array.field(static_cast<int>(field_index));
+    return comparators_[field_index]->Compare(*field, *field, offset, leftrowidx,
+                                              rightrowidx);
+  }
+
+  // StructArray Compare overload for different struct arrays
+  int Compare(StructArray const& array_left, StructArray const& array_right,
+              uint64_t field_index, uint64_t offset, uint64_t leftrowidx,
+              uint64_t rightrowidx) {
+    std::shared_ptr<Array> field_left = array_left.field(static_cast<int>(field_index));
+    std::shared_ptr<Array> field_right = array_right.field(static_cast<int>(field_index));
+    return comparators_[field_index]->Compare(*field_left, *field_right, offset,
+                                              leftrowidx, rightrowidx);
+  }
+
+  // StructArray Prepare overload
+  Status Prepare(StructArray const& array) {
+    auto fields = array.fields();
+    for (auto field = fields.begin(); field != fields.end(); field++) {
+      std::shared_ptr<DataType> physical_type = GetPhysicalType((*field)->type());
+      NestedComparatorFactory comparator_factory = NestedComparatorFactory();
+      std::shared_ptr<NestedValueComparator> current_field_comparator;
+      ARROW_ASSIGN_OR_RAISE(
+          current_field_comparator,
+          NestedComparatorFactory().MakeFieldComparator(*physical_type));
+      comparators_.push_back(current_field_comparator);
+    }
+    return Status::OK();
+  }
+
+ private:
+  struct NestedValueComparator {
+    virtual int Compare(Array const& left_array, Array const& right_array,
+                        uint64_t offset, uint64_t leftidx, uint64_t rightidx) = 0;
+
+    virtual ~NestedValueComparator() = default;
+  };
+
+  template <typename Type>
+  struct ConcreteNestedValueComparator : NestedValueComparator {
+    using FieldArrayType = typename TypeTraits<Type>::ArrayType;
+    using GetView = GetViewType<Type>;
+
+    virtual int Compare(Array const& left_array, Array const& right_array,
+                        uint64_t offset, uint64_t leftidx, uint64_t rightidx) {
+      const FieldArrayType& left_values = checked_cast<const FieldArrayType&>(left_array);
+      const FieldArrayType& right_values =
+          checked_cast<const FieldArrayType&>(right_array);
+      auto left_value = GetView::LogicalValue(left_values.GetView(leftidx - offset));
+      auto right_value = GetView::LogicalValue(right_values.GetView(rightidx - offset));
+
+      if (left_value == right_value)
+        return 0;
+      else if (left_value < right_value)
+        return -1;
+      else
+        return 1;
+    }
+  };
+
+  /**
+   * Internal use factory whose purpose is to detect the right type
+   * of comparator that should be built to be able to compare two
+   * nested values in the same field or column
+   */
+  struct NestedComparatorFactory {
+    Result<std::shared_ptr<NestedValueComparator>> MakeFieldComparator(
+        DataType const& physical_type) {
+      RETURN_NOT_OK(VisitTypeInline(physical_type, this));
+      DCHECK_NE(current_field_comparator_, nullptr);
+      return std::move(current_field_comparator_);
+    }
+
+#define VISIT(TYPE) \
+  Status Visit(const TYPE& type) { return VisitGeneric(type); }
+
+    VISIT_SORTABLE_PHYSICAL_TYPES(VISIT)
+#undef VISIT
+
+    Status Visit(const DataType& type) {
+      return Status::TypeError("Unsupported type for NestedComparatorFactory: ",
+                               type.ToString());
+    }
+
+    template <typename Type>
+    Status VisitGeneric(const Type&) {
+      current_field_comparator_ = std::shared_ptr<NestedValueComparator>(
+          new ConcreteNestedValueComparator<Type>());
+      return Status::OK();
+    }
+
+    std::shared_ptr<NestedValueComparator> current_field_comparator_;
+  };
+
+  std::vector<std::shared_ptr<NestedValueComparator>> comparators_;
+};
+
+template <typename ArrayType>
+struct ResolvedChunkComparator {
+  bool Compare(const ChunkedArrayResolver& chunk_resolver, uint64_t left,
+               uint64_t right) {
+    const auto chunk_left = chunk_resolver.Resolve<ArrayType>(left);
+    const auto chunk_right = chunk_resolver.Resolve<ArrayType>(right);
+    return chunk_left.Value() < chunk_right.Value();
+  }
+};
+
+template <>
+struct ResolvedChunkComparator<StructArray> {
+  bool Compare(const ChunkedArrayResolver& chunk_resolver, uint64_t left,
+               uint64_t right) {
+    const auto chunk_left = chunk_resolver.Resolve<StructArray>(left);
+    const auto chunk_right = chunk_resolver.Resolve<StructArray>(right);
+    NestedValuesComparator nested_values_comparator;
+    auto status = nested_values_comparator.Prepare(*chunk_left.array);
+
+    if (!status.ok()) {
+      return false;
+    }
+
+    for (int field_index = 0; field_index < chunk_left.array->num_fields();
+         field_index++) {
+      int val = nested_values_comparator.Compare(*(chunk_left.array),
+                                                 *(chunk_right.array), field_index, 0,
+                                                 chunk_left.index, chunk_right.index);
+
+      if (val == 0) {
+        // if field values are equal, check next field
+        continue;
+      }
+
+      return val == -1;
+    }
+
+    return false;
+  }
+};
+
 }  // namespace internal
 }  // namespace compute
 }  // namespace arrow
diff --git a/python/pyarrow/array.pxi b/python/pyarrow/array.pxi
index f5b3e7963f6..326f3006a3c 100644
--- a/python/pyarrow/array.pxi
+++ b/python/pyarrow/array.pxi
@@ -1402,6 +1402,22 @@ cdef class Array(_PandasConvertible):
         """
         return _pc().index(self, value, start, end, memory_pool=memory_pool)
 
+    def sort(self, order="ascending"):
+        """
+        Sort the Array
+
+        Parameters
+        ----------
+        order : "ascending" or "descending"
+            The order of the sorting.
+
+        Returns
+        -------
+        result : Array
+        """
+        indices = _pc().sort_indices(self, sort_keys=[("", order)])
+        return self.take(indices)
+
     def _to_pandas(self, options, types_mapper=None, **kwargs):
         return _array_like_to_pandas(self, options, types_mapper=types_mapper)
 
@@ -2746,6 +2762,29 @@ cdef class StructArray(Array):
         result.validate()
         return result
 
+    def sort(self, order="ascending", fieldname=None):
+        """
+        Sort the StructArray
+
+        Parameters
+        ----------
+        order : "ascending" or "descending"
+            The order of the sorting.
+        fieldname : str or None, default None
+            If to sort the array by one of its fields
+            or by the whole array.
+
+        Returns
+        -------
+        result : StructArray
+        """
+        if fieldname is not None:
+            tosort = self.field(fieldname)
+        else:
+            tosort = self
+        indices = _pc().sort_indices(tosort, sort_keys=[("", order)])
+        return self.take(indices)
+
 
 cdef class ExtensionArray(Array):
     """
diff --git a/python/pyarrow/table.pxi b/python/pyarrow/table.pxi
index 30352bf3950..32c981152fa 100644
--- a/python/pyarrow/table.pxi
+++ b/python/pyarrow/table.pxi
@@ -433,6 +433,22 @@ cdef class ChunkedArray(_PandasConvertible):
 
         return result
 
+    def sort(self, order="ascending"):
+        """
+        Sort the ChunkedArray
+
+        Parameters
+        ----------
+        order : "ascending" or "descending"
+            The order of the sorting.
+
+        Returns
+        -------
+        result : ChunkedArray
+        """
+        indices = _pc().sort_indices(self, sort_keys=[("", order)])
+        return self.take(indices)
+
     def _to_pandas(self, options, types_mapper=None, **kwargs):
         return _array_like_to_pandas(self, options, types_mapper=types_mapper)
 
diff --git a/python/pyarrow/tests/test_array.py b/python/pyarrow/tests/test_array.py
index 154ca348d2b..cc018d07731 100644
--- a/python/pyarrow/tests/test_array.py
+++ b/python/pyarrow/tests/test_array.py
@@ -725,6 +725,159 @@ def test_struct_array_from_chunked():
         pa.StructArray.from_arrays([chunked_arr], ["foo"])
 
 
+def test_array_sort():
+    arr = pa.array([5, 7, 35], type=pa.int64())
+    sorted_arr = arr.sort("descending")
+    assert sorted_arr.to_pylist() == [35, 7, 5]
+
+    arr = pa.chunked_array([[1, 2, 3], [4, 5, 6]])
+    sorted_arr = arr.sort("descending")
+    assert sorted_arr.to_pylist() == [6, 5, 4, 3, 2, 1]
+
+
+def test_struct_array_sort():
+    arr = pa.StructArray.from_arrays([
+        pa.array([5, 7, 7, 35], type=pa.int64()),
+        pa.array(["foo", "car", "bar", "foobar"])
+    ], names=["a", "b"])
+
+    sorted_arr = arr.sort("descending", fieldname="a")
+    assert sorted_arr.to_pylist() == [
+        {"a": 35, "b": "foobar"},
+        {"a": 7, "b": "car"},
+        {"a": 7, "b": "bar"},
+        {"a": 5, "b": "foo"},
+    ]
+
+    sorted_arr = arr.sort("descending")
+    assert sorted_arr.to_pylist() == [
+        {"a": 35, "b": "foobar"},
+        {"a": 7, "b": "car"},
+        {"a": 7, "b": "bar"},
+        {"a": 5, "b": "foo"},
+    ]
+
+    sorted_arr = arr.sort("ascending")
+    assert sorted_arr.to_pylist() == [
+        {"a": 5, "b": "foo"},
+        {"a": 7, "b": "bar"},
+        {"a": 7, "b": "car"},
+        {"a": 35, "b": "foobar"},
+    ]
+
+
+def test_struct_chunked_array_sort():
+    arr1 = pa.StructArray.from_arrays([
+        pa.array([5, 7, 8], type=pa.int64()),
+        pa.array(["foo", "car", "far"])
+    ], names=["a", "b"])
+
+    arr2 = pa.StructArray.from_arrays([
+        pa.array([7, 35, 9], type=pa.int64()),
+        pa.array(["bar", "foobar", "tar"])
+    ], names=["a", "b"])
+
+    chunked_arr = pa.chunked_array([arr1, arr2])
+
+    sorted_arr = chunked_arr.sort("descending")
+    assert sorted_arr.to_pylist() == [
+        {"a": 35, "b": "foobar"},
+        {"a": 9, "b": "tar"},
+        {"a": 8, "b": "far"},
+        {"a": 7, "b": "car"},
+        {"a": 7, "b": "bar"},
+        {"a": 5, "b": "foo"},
+    ]
+
+    sorted_arr = chunked_arr.sort("ascending")
+    assert sorted_arr.to_pylist() == [
+        {"a": 5, "b": "foo"},
+        {"a": 7, "b": "bar"},
+        {"a": 7, "b": "car"},
+        {"a": 8, "b": "far"},
+        {"a": 9, "b": "tar"},
+        {"a": 35, "b": "foobar"},
+    ]
+
+    arr1 = pa.StructArray.from_arrays([
+        pa.array(["foo", "car", "tar"]),
+        pa.array([5, 7, 8], type=pa.int64())
+    ], names=["a", "b"])
+
+    arr2 = pa.StructArray.from_arrays([
+        pa.array(["bar", "foobar", "far"]),
+        pa.array([7, 35, 9], type=pa.int64())
+    ], names=["a", "b"])
+
+    chunked_arr = pa.chunked_array([arr1, arr2])
+
+    sorted_arr = chunked_arr.sort("ascending")
+    assert sorted_arr.to_pylist() == [
+        {"a": "bar", "b": 7},
+        {"a": "car", "b": 7},
+        {"a": "far", "b": 9},
+        {"a": "foo", "b": 5},
+        {"a": "foobar", "b": 35},
+        {"a": "tar", "b": 8},
+    ]
+
+    sorted_arr = chunked_arr.sort("descending")
+    assert sorted_arr.to_pylist() == [
+        {"a": "tar", "b": 8},
+        {"a": "foobar", "b": 35},
+        {"a": "foo", "b": 5},
+        {"a": "far", "b": 9},
+        {"a": "car", "b": 7},
+        {"a": "bar", "b": 7},
+    ]
+
+    arr1 = pa.StructArray.from_arrays([
+        pa.array([5, 5, 5], type=pa.int64()),
+        pa.array([3, 2, 2], type=pa.int64()),
+        pa.array(["foo", "car", "tar"])
+    ], names=["a", "b", "c"])
+
+    arr2 = pa.StructArray.from_arrays([
+        pa.array([5, 5, 2], type=pa.int64()),
+        pa.array([2, 8, 3], type=pa.int64()),
+        pa.array(["bar", "foobar", "far"])
+    ], names=["a", "b", "c"])
+
+    arr3 = pa.StructArray.from_arrays([
+        pa.array([5, 5, 2], type=pa.int64()),
+        pa.array([2, 8, 1], type=pa.int64()),
+        pa.array(["cat", "dog", "mouse"])
+    ], names=["a", "b", "c"])
+
+    chunked_arr = pa.chunked_array([arr1, arr2, arr3])
+
+    sorted_arr = chunked_arr.sort("ascending")
+    assert sorted_arr.to_pylist() == [
+        {"a": 2, "b": 1, "c": "mouse"},
+        {"a": 2, "b": 3, "c": "far"},
+        {"a": 5, "b": 2, "c": "bar"},
+        {"a": 5, "b": 2, "c": "car"},
+        {"a": 5, "b": 2, "c": "cat"},
+        {"a": 5, "b": 2, "c": "tar"},
+        {"a": 5, "b": 3, "c": "foo"},
+        {"a": 5, "b": 8, "c": "dog"},
+        {"a": 5, "b": 8, "c": "foobar"}
+    ]
+
+    sorted_arr = chunked_arr.sort("descending")
+    assert sorted_arr.to_pylist() == [
+        {"a": 5, "b": 8, "c": "foobar"},
+        {"a": 5, "b": 8, "c": "dog"},
+        {"a": 5, "b": 3, "c": "foo"},
+        {"a": 5, "b": 2, "c": "tar"},
+        {"a": 5, "b": 2, "c": "cat"},
+        {"a": 5, "b": 2, "c": "car"},
+        {"a": 5, "b": 2, "c": "bar"},
+        {"a": 2, "b": 3, "c": "far"},
+        {"a": 2, "b": 1, "c": "mouse"}
+    ]
+
+
 @pytest.mark.parametrize("offset", (0, 1))
 def test_dictionary_from_buffers(offset):
     a = pa.array(["one", "two", "three", "two", "one"]).dictionary_encode()