diff --git a/cpp/src/arrow/array/array_dict.h b/cpp/src/arrow/array/array_dict.h
index 8791eaa07db..676ab87b8f3 100644
--- a/cpp/src/arrow/array/array_dict.h
+++ b/cpp/src/arrow/array/array_dict.h
@@ -111,6 +111,10 @@ class ARROW_EXPORT DictionaryArray : public Array {
 
   const DictionaryType* dict_type() const { return dict_type_; }
 
+  bool IsNull(int64_t i) const {
+    return indices_->IsNull(i) || dictionary()->IsNull(GetValueIndex(i));
+  }
+
  private:
   void SetData(const std::shared_ptr<ArrayData>& data);
   const DictionaryType* dict_type_;
diff --git a/cpp/src/arrow/compute/kernels/vector_array_sort.cc b/cpp/src/arrow/compute/kernels/vector_array_sort.cc
index 324a435441f..8d55c645084 100644
--- a/cpp/src/arrow/compute/kernels/vector_array_sort.cc
+++ b/cpp/src/arrow/compute/kernels/vector_array_sort.cc
@@ -173,6 +173,78 @@ class ArrayCompareSorter {
   }
 };
 
+template <>
+class ArrayCompareSorter<DictionaryType> {
+ public:
+  NullPartitionResult operator()(uint64_t* indices_begin, uint64_t* indices_end,
+                                 const Array& array, int64_t offset,
+                                 const ArraySortOptions& options) {
+    const auto& dict_array = checked_cast<const DictionaryArray&>(array);
+    const auto& dict_values = dict_array.dictionary();
+    const auto& dict_indices = dict_array.indices();
+
+    // Algorithm:
+    // 1) Use the Rank function to get an exactly-equivalent-order array
+    //    of the dictionary values, but with a datatype that's friendlier to
+    //    sorting (uint64).
+    // 2) Act as if we were sorting a dictionary array with the same indices,
+    //    but with the ranks as dictionary values.
+    // 2a) Dictionary-decode the ranks by calling Take.
+    // 2b) Sort the decoded ranks. Not only those are uint64, they are dense
+    //     in a [0, k) range where k is the number of unique dictionary values.
+    //     Therefore, unless the dictionary is very large, a fast counting sort
+    //     will be used.
+    //
+    // The bottom line is that performance will usually be much better
+    // (potentially an order of magnitude faster) than by naively decoding
+    // the original dictionary and sorting the decoded version.
+
+    // TODO special-case all-nulls arrays to avoid ranking and decoding them?
+
+    // FIXME Should be able to use the caller's KernelContext for rank() and take()
+
+    // FIXME Propagate errors instead of aborting
+    auto ranks = *RanksWithNulls(dict_values);
+
+    auto decoded_ranks = *Take(*ranks, *dict_indices);
+
+    auto rank_sorter = *GetArraySorter(*decoded_ranks->type() /* should be uint64 */);
+    return rank_sorter(indices_begin, indices_end, *decoded_ranks, offset, options);
+  }
+
+ private:
+  Result<std::shared_ptr<Array>> RanksWithNulls(const std::shared_ptr<Array>& array) {
+    // Notes:
+    // * The order is always ascending here, since the goal is to produce
+    //   an exactly-equivalent-order of the dictionary values.
+    // * We're going to re-emit nulls in the output, so we can just always consider
+    //   them "at the end".  Note that choosing AtStart would merely shift other
+    //   ranks by 1 if there are any nulls...
+    RankOptions rank_options(SortOrder::Ascending, NullPlacement::AtEnd,
+                             RankOptions::Dense);
+
+    // XXX Should this support Type::NA?
+    auto data = array->data();
+    std::shared_ptr<Buffer> null_bitmap;
+    if (array->null_count() > 0) {
+      null_bitmap = array->null_bitmap();
+      data = array->data()->Copy();
+      data->buffers[0] = nullptr;
+      data->null_count = 0;
+      DCHECK_EQ(data->offset, 0);  // FIXME
+    }
+    ARROW_ASSIGN_OR_RAISE(auto rank_datum, CallFunction("rank", {array}, &rank_options));
+    auto rank_data = rank_datum.array();
+    DCHECK_EQ(rank_data->GetNullCount(), 0);
+    // If there were nulls in the input, paste them in the output
+    if (null_bitmap) {
+      rank_data->buffers[0] = std::move(null_bitmap);
+      rank_data->null_count = array->null_count();
+    }
+    return MakeArray(rank_data);
+  }
+};
+
 template <typename ArrowType>
 class ArrayCountSorter {
   using ArrayType = typename TypeTraits<ArrowType>::ArrayType;
@@ -405,7 +477,8 @@ struct ArraySorter<Type, enable_if_t<is_integer_type<Type>::value &&
 template <typename Type>
 struct ArraySorter<
     Type, enable_if_t<is_floating_type<Type>::value || is_base_binary_type<Type>::value ||
-                      is_fixed_size_binary_type<Type>::value>> {
+                      is_fixed_size_binary_type<Type>::value ||
+                      is_dictionary_type<Type>::value>> {
   ArrayCompareSorter<Type> impl;
 };
 
@@ -507,6 +580,13 @@ void AddArraySortingKernels(VectorKernel base, VectorFunction* func) {
   DCHECK_OK(func->AddKernel(base));
 }
 
+template <template <typename...> class ExecTemplate>
+void AddDictArraySortingKernels(VectorKernel base, VectorFunction* func) {
+  base.signature = KernelSignature::Make({Type::DICTIONARY}, uint64());
+  base.exec = ExecTemplate<UInt64Type, DictionaryType>::Exec;
+  DCHECK_OK(func->AddKernel(base));
+}
+
 const ArraySortOptions* GetDefaultArraySortOptions() {
   static const auto kDefaultArraySortOptions = ArraySortOptions::Defaults();
   return &kDefaultArraySortOptions;
@@ -561,6 +641,7 @@ void RegisterVectorArraySort(FunctionRegistry* registry) {
   base.init = ArraySortIndicesState::Init;
   base.exec_chunked = ArraySortIndicesChunked;
   AddArraySortingKernels<ArraySortIndices>(base, array_sort_indices.get());
+  AddDictArraySortingKernels<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 28307ecca37..872f3f06404 100644
--- a/cpp/src/arrow/compute/kernels/vector_sort.cc
+++ b/cpp/src/arrow/compute/kernels/vector_sort.cc
@@ -374,8 +374,8 @@ class ConcreteRecordBatchColumnSorter : public RecordBatchColumnSorter {
     } else {
       // NOTE that null_count_ is merely an upper bound on the number of nulls
       // in this particular range.
-      p = PartitionNullsOnly<StablePartitioner>(indices_begin, indices_end, array_,
-                                                offset, null_placement_);
+      p = PartitionNullsOnly<ArrayType, StablePartitioner>(
+          indices_begin, indices_end, array_, offset, null_placement_);
       DCHECK_LE(p.nulls_end - p.nulls_begin, null_count_);
     }
     const NullPartitionResult q = PartitionNullLikes<ArrayType, StablePartitioner>(
@@ -797,8 +797,8 @@ class MultipleKeyRecordBatchSorter : public TypeVisitor {
     using ArrayType = typename TypeTraits<Type>::ArrayType;
     const ArrayType& array = checked_cast<const ArrayType&>(first_sort_key.array);
 
-    const auto p = PartitionNullsOnly<StablePartitioner>(indices_begin_, indices_end_,
-                                                         array, 0, null_placement_);
+    const auto p = PartitionNullsOnly<ArrayType, StablePartitioner>(
+        indices_begin_, indices_end_, array, 0, null_placement_);
     const auto q = PartitionNullLikes<ArrayType, StablePartitioner>(
         p.non_nulls_begin, p.non_nulls_end, array, 0, null_placement_);
 
diff --git a/cpp/src/arrow/compute/kernels/vector_sort_benchmark.cc b/cpp/src/arrow/compute/kernels/vector_sort_benchmark.cc
index 6ab0bcfde97..e3604599ee5 100644
--- a/cpp/src/arrow/compute/kernels/vector_sort_benchmark.cc
+++ b/cpp/src/arrow/compute/kernels/vector_sort_benchmark.cc
@@ -27,13 +27,17 @@
 
 namespace arrow {
 namespace compute {
+
 constexpr auto kSeed = 0x0ff1ce;
+constexpr int32_t kDictionarySize = 20;  // a typical dictionary size
 
 static void ArraySortIndicesBenchmark(benchmark::State& state,
                                       const std::shared_ptr<Array>& values) {
   for (auto _ : state) {
     ABORT_NOT_OK(SortIndices(*values).status());
   }
+  // This may be redundant with the SetItemsProcessed() call in RegressionArgs,
+  // if size_is_bytes was false.
   state.SetItemsProcessed(state.iterations() * values->length());
 }
 
@@ -56,6 +60,51 @@ static void ArraySortIndicesInt64Benchmark(benchmark::State& state, int64_t min,
   ArraySortIndicesBenchmark(state, values);
 }
 
+static void ArraySortIndicesInt64DictBenchmark(benchmark::State& state, int64_t min,
+                                               int64_t max) {
+  RegressionArgs args(state);
+
+  const int64_t array_size = args.size / sizeof(int64_t);
+
+  auto rand = random::RandomArrayGenerator(kSeed);
+  auto dict_values = rand.Int64(kDictionarySize, min, max, args.null_proportion / 2);
+  auto dict_indices =
+      rand.Int64(array_size, 0, kDictionarySize - 1, args.null_proportion / 2);
+  auto dict_array = *DictionaryArray::FromArrays(dict_indices, dict_values);
+
+  ArraySortIndicesBenchmark(state, dict_array);
+}
+
+static void ArraySortIndicesStringsBenchmark(benchmark::State& state) {
+  RegressionArgs args(state, /*size_is_bytes=*/false);
+  // XXX This division to make numbers comparable with ArraySortIndicesInt64Benchmark
+  // (including the SetItemsProcessed() call in the RegressionArgs destructor)
+  args.size /= sizeof(int64_t);
+
+  const int64_t array_size = args.size;
+  auto rand = random::RandomArrayGenerator(kSeed);
+  auto values =
+      rand.String(array_size, /*min_length=*/3, /*max_length=*/25, args.null_proportion);
+
+  ArraySortIndicesBenchmark(state, values);
+}
+
+static void ArraySortIndicesStringsDictBenchmark(benchmark::State& state) {
+  RegressionArgs args(state, /*size_is_bytes=*/false);
+  // XXX Same as in ArraySortIndicesStringsBenchmark above
+  args.size /= sizeof(int64_t);
+
+  const int64_t array_size = args.size;
+  auto rand = random::RandomArrayGenerator(kSeed);
+  auto dict_values = rand.String(kDictionarySize, /*min_length=*/3, /*max_length=*/25,
+                                 args.null_proportion / 2);
+  auto dict_indices =
+      rand.Int64(array_size, 0, kDictionarySize - 1, args.null_proportion / 2);
+  auto dict_array = *DictionaryArray::FromArrays(dict_indices, dict_values);
+
+  ArraySortIndicesBenchmark(state, dict_array);
+}
+
 static void ChunkedArraySortIndicesInt64Benchmark(benchmark::State& state, int64_t min,
                                                   int64_t max) {
   RegressionArgs args(state);
@@ -81,6 +130,20 @@ static void ArraySortIndicesInt64Wide(benchmark::State& state) {
   ArraySortIndicesInt64Benchmark(state, min, max);
 }
 
+static void ArraySortIndicesInt64Dict(benchmark::State& state) {
+  const auto min = std::numeric_limits<int64_t>::min();
+  const auto max = std::numeric_limits<int64_t>::max();
+  ArraySortIndicesInt64DictBenchmark(state, min, max);
+}
+
+static void ArraySortIndicesStrings(benchmark::State& state) {
+  ArraySortIndicesStringsBenchmark(state);
+}
+
+static void ArraySortIndicesStringsDict(benchmark::State& state) {
+  ArraySortIndicesStringsDictBenchmark(state);
+}
+
 static void ArraySortIndicesBool(benchmark::State& state) {
   RegressionArgs args(state);
 
@@ -249,6 +312,24 @@ BENCHMARK(ArraySortIndicesInt64Wide)
     ->Args({1 << 23, 100})
     ->Unit(benchmark::TimeUnit::kNanosecond);
 
+BENCHMARK(ArraySortIndicesInt64Dict)
+    ->Apply(RegressionSetArgs)
+    ->Args({1 << 20, 100})
+    ->Args({1 << 23, 100})
+    ->Unit(benchmark::TimeUnit::kNanosecond);
+
+BENCHMARK(ArraySortIndicesStrings)
+    ->Apply(RegressionSetArgs)
+    ->Args({1 << 20, 100})
+    ->Args({1 << 23, 100})
+    ->Unit(benchmark::TimeUnit::kNanosecond);
+
+BENCHMARK(ArraySortIndicesStringsDict)
+    ->Apply(RegressionSetArgs)
+    ->Args({1 << 20, 100})
+    ->Args({1 << 23, 100})
+    ->Unit(benchmark::TimeUnit::kNanosecond);
+
 BENCHMARK(ArraySortIndicesBool)
     ->Apply(RegressionSetArgs)
     ->Args({1 << 20, 100})
diff --git a/cpp/src/arrow/compute/kernels/vector_sort_internal.h b/cpp/src/arrow/compute/kernels/vector_sort_internal.h
index d8b024525c8..e914564d08f 100644
--- a/cpp/src/arrow/compute/kernels/vector_sort_internal.h
+++ b/cpp/src/arrow/compute/kernels/vector_sort_internal.h
@@ -191,9 +191,9 @@ struct NullPartitionResult {
 // Move nulls (not null-like values) to end of array.
 //
 // `offset` is used when this is called on a chunk of a chunked array
-template <typename Partitioner>
+template <typename ArrayType, typename Partitioner>
 NullPartitionResult PartitionNullsOnly(uint64_t* indices_begin, uint64_t* indices_end,
-                                       const Array& values, int64_t offset,
+                                       const ArrayType& values, int64_t offset,
                                        NullPlacement null_placement) {
   if (values.null_count() == 0) {
     return NullPartitionResult::NoNulls(indices_begin, indices_end, null_placement);
@@ -254,8 +254,8 @@ NullPartitionResult PartitionNulls(uint64_t* indices_begin, uint64_t* indices_en
                                    const ArrayType& values, int64_t offset,
                                    NullPlacement null_placement) {
   // Partition nulls at start (resp. end), and null-like values just before (resp. after)
-  NullPartitionResult p = PartitionNullsOnly<Partitioner>(indices_begin, indices_end,
-                                                          values, offset, null_placement);
+  NullPartitionResult p = PartitionNullsOnly<ArrayType, Partitioner>(
+      indices_begin, indices_end, values, offset, null_placement);
   NullPartitionResult q = PartitionNullLikes<ArrayType, Partitioner>(
       p.non_nulls_begin, p.non_nulls_end, values, offset, null_placement);
   return NullPartitionResult{q.non_nulls_begin, q.non_nulls_end,
diff --git a/cpp/src/arrow/compute/kernels/vector_sort_test.cc b/cpp/src/arrow/compute/kernels/vector_sort_test.cc
index c32b1a1e591..7a1669c401e 100644
--- a/cpp/src/arrow/compute/kernels/vector_sort_test.cc
+++ b/cpp/src/arrow/compute/kernels/vector_sort_test.cc
@@ -354,6 +354,77 @@ TEST(ArraySortIndicesFunction, Array) {
   AssertDatumsEqual(expected, actual, /*verbose=*/true);
 }
 
+TEST(ArraySortIndicesFunction, DictionaryArray) {
+  // Decoded dictionary array:
+  // (["b", "c", null, null, null, "b", "c", "c", "a"])
+
+  std::vector<std::string> expected_str = {
+      "[8, 0, 5, 1, 6, 7, 2, 3, 4]",  // SortOrder::Ascending NullPlacement::AtEnd
+      "[2, 3, 4, 8, 0, 5, 1, 6, 7]",  // SortOrder::Ascending NullPlacement::AtStart
+      "[1, 6, 7, 0, 5, 8, 2, 3, 4]",  // SortOrder::Descending NullPlacement::AtEnd
+      "[2, 3, 4, 1, 6, 7, 0, 5, 8]"   // SortOrder::Descending NullPlacement::AtStart
+  };
+
+  for (auto index_type : all_dictionary_index_types()) {
+    ARROW_SCOPED_TRACE("index_type = ", index_type->ToString());
+    int i = 0;
+    auto dict_arr = DictArrayFromJSON(dictionary(index_type, utf8()),
+                                      "[0, 4, null, 1, null, 0, 4, 2, 3]",
+                                      "[ \"b\", null, \"c\", \"a\", \"c\"]");
+    for (auto order : AllOrders()) {
+      for (auto null_placement : AllNullPlacements()) {
+        ARROW_SCOPED_TRACE("i = ", i);
+        ArraySortOptions options{order, null_placement};
+        auto expected = ArrayFromJSON(uint64(), expected_str[i++]);
+        ASSERT_OK_AND_ASSIGN(auto actual,
+                             CallFunction("array_sort_indices", {dict_arr}, &options));
+        ValidateOutput(actual);
+        AssertDatumsEqual(expected, actual, /*verbose=*/true);
+      }
+    }
+  }
+}
+
+Result<std::shared_ptr<Array>> DecodeDictionary(const Array& array) {
+  const auto& dict_array = checked_cast<const DictionaryArray&>(array);
+  ARROW_ASSIGN_OR_RAISE(auto decoded_datum,
+                        Take(dict_array.dictionary(), dict_array.indices()));
+  return decoded_datum.make_array();
+}
+
+TEST(ArraySortIndicesFunction, RandomDictionaryArray) {
+  ::arrow::random::RandomArrayGenerator rng(/*seed=*/1234);
+  constexpr int64_t kLength = 200;
+  constexpr int64_t kDictLength = 20;
+
+  // Ensure there are duplicates in the dictionary and the indices,
+  // and nulls in both as well.
+  auto dict_values = rng.StringWithRepeats(kDictLength, /*unique=*/kDictLength / 2,
+                                           /*min_length=*/1, /*max_length=*/10,
+                                           /*null_probability=*/0.2);
+  auto dict_indices = rng.Int64(kLength, 0, kDictLength - 1, /*null_probability = */ 0.2);
+  ASSERT_OK_AND_ASSIGN(auto dict_array,
+                       DictionaryArray::FromArrays(dict_indices, dict_values));
+  ASSERT_OK_AND_ASSIGN(auto decoded, DecodeDictionary(*dict_array));
+
+  for (auto order : AllOrders()) {
+    for (auto null_placement : AllNullPlacements()) {
+      ArraySortOptions options{order, null_placement};
+      // Sorting the dictionary array...
+      ASSERT_OK_AND_ASSIGN(auto actual,
+                           CallFunction("array_sort_indices", {dict_array}, &options));
+      ValidateOutput(actual);
+
+      // should give identical results to sorting the decoded array
+      ASSERT_OK_AND_ASSIGN(auto expected,
+                           CallFunction("array_sort_indices", {decoded}, &options));
+      AssertDatumsEqual(expected, actual, /*verbose=*/true);
+    }
+  }
+
+  // TODO test with sliced dict indices and values...
+}
+
 TEST(ArraySortIndicesFunction, ChunkedArray) {
   auto arr = ChunkedArrayFromJSON(int16(), {"[0, 1]", "[null, -3, null, -42, 5]"});
   auto expected = ChunkedArrayFromJSON(uint64(), {"[5, 3, 0, 1, 6, 2, 4]"});
diff --git a/cpp/src/arrow/util/benchmark_util.h b/cpp/src/arrow/util/benchmark_util.h
index 79484989ac5..15f2ea94fe4 100644
--- a/cpp/src/arrow/util/benchmark_util.h
+++ b/cpp/src/arrow/util/benchmark_util.h
@@ -104,7 +104,7 @@ void RegressionSetArgs(benchmark::internal::Benchmark* bench) {
 // RAII struct to handle some of the boilerplate in regression benchmarks
 struct RegressionArgs {
   // size of memory tested (per iteration) in bytes
-  const int64_t size;
+  int64_t size;
 
   // proportion of nulls in generated arrays
   double null_proportion;