diff --git a/python/pyarrow/array.pxi b/python/pyarrow/array.pxi
index 46e94b4f4b3..c132269c563 100644
--- a/python/pyarrow/array.pxi
+++ b/python/pyarrow/array.pxi
@@ -244,12 +244,22 @@ cdef class Schema:
     def __len__(self):
         return self.schema.num_fields()
 
-    def __getitem__(self, i):
-        if i < 0 or i >= len(self):
-            raise IndexError("{0} is out of bounds".format(i))
+    def __getitem__(self, int64_t i):
+
+        cdef:
+            Field result = Field()
+            int64_t num_fields = self.schema.num_fields()
+            int64_t index
+
+        if not -num_fields <= i < num_fields:
+            raise IndexError(
+                'Schema field index {:d} is out of range'.format(i)
+            )
+
+        index = i if i >= 0 else num_fields + i
+        assert index >= 0
 
-        cdef Field result = Field()
-        result.init(self.schema.field(i))
+        result.init(self.schema.field(index))
         result.type = pyarrow_wrap_data_type(result.field.type())
 
         return result
diff --git a/python/pyarrow/table.pxi b/python/pyarrow/table.pxi
index 8dd18cf4136..bd8cce41400 100644
--- a/python/pyarrow/table.pxi
+++ b/python/pyarrow/table.pxi
@@ -762,24 +762,37 @@ cdef class Table:
         """
         return pyarrow_wrap_schema(self.table.schema())
 
-    def column(self, index):
+    def column(self, int64_t i):
         """
         Select a column by its numeric index.
 
         Parameters
         ----------
-        index: int
+        i : int
 
         Returns
         -------
         pyarrow.Column
         """
         self._check_nullptr()
-        cdef Column column = Column()
+
+        cdef:
+            Column column = Column()
+            int64_t num_columns = self.num_columns
+            int64_t index
+
+        if not -num_columns <= i < num_columns:
+            raise IndexError(
+                'Table column index {:d} is out of range'.format(i)
+            )
+
+        index = i if i >= 0 else num_columns + i
+        assert index >= 0
+
         column.init(self.table.column(index))
         return column
 
-    def __getitem__(self, i):
+    def __getitem__(self, int64_t i):
         return self.column(i)
 
     def itercolumns(self):
diff --git a/python/pyarrow/tests/test_schema.py b/python/pyarrow/tests/test_schema.py
index 2d98865b56e..a6fe1a5df0e 100644
--- a/python/pyarrow/tests/test_schema.py
+++ b/python/pyarrow/tests/test_schema.py
@@ -212,3 +212,23 @@ def test_schema_equals():
     del fields[-1]
     sch3 = pa.schema(fields)
     assert not sch1.equals(sch3)
+
+
+def test_schema_negative_indexing():
+    fields = [
+        pa.field('foo', pa.int32()),
+        pa.field('bar', pa.string()),
+        pa.field('baz', pa.list_(pa.int8()))
+    ]
+
+    schema = pa.schema(fields)
+
+    assert schema[-1].equals(schema[2])
+    assert schema[-2].equals(schema[1])
+    assert schema[-3].equals(schema[0])
+
+    with pytest.raises(IndexError):
+        schema[-4]
+
+    with pytest.raises(IndexError):
+        schema[3]
diff --git a/python/pyarrow/tests/test_table.py b/python/pyarrow/tests/test_table.py
index 0567e8aba68..72ce6967edf 100644
--- a/python/pyarrow/tests/test_table.py
+++ b/python/pyarrow/tests/test_table.py
@@ -254,3 +254,24 @@ def test_table_pandas():
     assert set(df.columns) == set(('a', 'b'))
     assert df.shape == (5, 2)
     assert df.loc[0, 'b'] == -10
+
+
+def test_table_negative_indexing():
+    data = [
+        pa.array(range(5)),
+        pa.array([-10, -5, 0, 5, 10]),
+        pa.array([1.0, 2.0, 3.0]),
+        pa.array(['ab', 'bc', 'cd']),
+    ]
+    table = pa.Table.from_arrays(data, names=tuple('abcd'))
+
+    assert table[-1].equals(table[3])
+    assert table[-2].equals(table[2])
+    assert table[-3].equals(table[1])
+    assert table[-4].equals(table[0])
+
+    with pytest.raises(IndexError):
+        table[-5]
+
+    with pytest.raises(IndexError):
+        table[4]