diff --git a/python/pyarrow/pandas_compat.py b/python/pyarrow/pandas_compat.py
index b94abe4e2e6..efd6c892e7c 100644
--- a/python/pyarrow/pandas_compat.py
+++ b/python/pyarrow/pandas_compat.py
@@ -466,11 +466,20 @@ def _get_index_level(df, name):
     return df.index.get_level_values(key)
 
 
+def _level_name(name):
+    # preserve type when default serializable, otherwise str it
+    try:
+        json.dumps(name)
+        return name
+    except TypeError:
+        return str(name)
+
+
 def _get_range_index_descriptor(level):
     # public start/stop/step attributes added in pandas 0.25.0
     return {
         'kind': 'range',
-        'name': level.name,
+        'name': _level_name(level.name),
         'start': _pandas_api.get_rangeindex_attribute(level, 'start'),
         'stop': _pandas_api.get_rangeindex_attribute(level, 'stop'),
         'step': _pandas_api.get_rangeindex_attribute(level, 'step')
diff --git a/python/pyarrow/tests/test_pandas.py b/python/pyarrow/tests/test_pandas.py
index 5de84b30432..2165627ad08 100644
--- a/python/pyarrow/tests/test_pandas.py
+++ b/python/pyarrow/tests/test_pandas.py
@@ -4045,6 +4045,20 @@ def test_metadata_compat_missing_field_name():
     tm.assert_frame_equal(result, expected, check_like=True)
 
 
+def test_metadata_index_name_not_json_serializable():
+    name = np.int64(6)  # not json serializable by default
+    table = pa.table(pd.DataFrame(index=pd.RangeIndex(0, 4, name=name)))
+    metadata = table.schema.pandas_metadata
+    assert metadata['index_columns'][0]['name'] == '6'
+
+
+def test_metadata_index_name_is_json_serializable():
+    name = 6  # json serializable by default
+    table = pa.table(pd.DataFrame(index=pd.RangeIndex(0, 4, name=name)))
+    metadata = table.schema.pandas_metadata
+    assert metadata['index_columns'][0]['name'] == 6
+
+
 def make_df_with_timestamps():
     # Some of the milliseconds timestamps deliberately don't fit in the range
     # that is possible with nanosecond timestamps.