diff --git a/modin/backends/pandas/query_compiler.py b/modin/backends/pandas/query_compiler.py
index 181af801306..4d585658893 100644
--- a/modin/backends/pandas/query_compiler.py
+++ b/modin/backends/pandas/query_compiler.py
@@ -1562,6 +1562,7 @@ def sort_index(self, **kwargs):
         ):
             return self.default_to_pandas(
                 pandas.DataFrame.sort_index,
+                axis=axis,
                 level=level,
                 sort_remaining=sort_remaining,
                 **kwargs
diff --git a/modin/pandas/test/test_dataframe.py b/modin/pandas/test/test_dataframe.py
index a886151dc28..43786a5e2c9 100644
--- a/modin/pandas/test/test_dataframe.py
+++ b/modin/pandas/test/test_dataframe.py
@@ -5970,11 +5970,19 @@ def test_sort_index(self, data, axis, ascending, na_position, sort_remaining):
         pandas_df.index = pandas.MultiIndex.from_tuples(
             [(i // 10, i // 5, i) for i in range(len(pandas_df))]
         )
+        modin_df.columns = pd.MultiIndex.from_tuples(
+            [(i // 10, i // 5, i) for i in range(len(modin_df.columns))]
+        )
+        pandas_df.columns = pd.MultiIndex.from_tuples(
+            [(i // 10, i // 5, i) for i in range(len(pandas_df.columns))]
+        )
 
         with pytest.warns(UserWarning):
             df_equals(modin_df.sort_index(level=0), pandas_df.sort_index(level=0))
         with pytest.warns(UserWarning):
             df_equals(modin_df.sort_index(axis=0), pandas_df.sort_index(axis=0))
+        with pytest.warns(UserWarning):
+            df_equals(modin_df.sort_index(axis=1), pandas_df.sort_index(axis=1))
 
     @pytest.mark.parametrize("data", test_data_values, ids=test_data_keys)
     @pytest.mark.parametrize("axis", axis_values, ids=axis_keys)