diff --git a/python/cudf/cudf/core/dataframe.py b/python/cudf/cudf/core/dataframe.py
index f2e57d219e3..9fcbda741f6 100644
--- a/python/cudf/cudf/core/dataframe.py
+++ b/python/cudf/cudf/core/dataframe.py
@@ -2744,11 +2744,14 @@ def reindex(
         else:
             if columns is None:
                 columns = labels
-        df = (
-            self
-            if columns is None
-            else self[list(set(self._column_names) & set(columns))]
-        )
+        if columns is None:
+            df = self
+        else:
+            columns = as_index(columns)
+            intersection = self._data.to_pandas_index().intersection(
+                columns.to_pandas()
+            )
+            df = self.loc[:, intersection]
 
         return df._reindex(
             column_names=columns,
diff --git a/python/cudf/cudf/core/indexed_frame.py b/python/cudf/cudf/core/indexed_frame.py
index 86a8e64b213..dadfa16e52f 100644
--- a/python/cudf/cudf/core/indexed_frame.py
+++ b/python/cudf/cudf/core/indexed_frame.py
@@ -2584,7 +2584,7 @@ def _reindex(
         Parameters
         ----------
         columns_names : array-like
-            The list of columns to select from the Frame,
+            array-like of columns to select from the Frame,
             if ``columns`` is a superset of ``Frame.columns`` new
             columns are created.
         dtypes : dict
@@ -2646,9 +2646,35 @@ def _reindex(
                 df = df.take(index.argsort(ascending=True).argsort())
 
         index = index if index is not None else df.index
-        names = (
-            column_names if column_names is not None else list(df._data.names)
-        )
+
+        if column_names is None:
+            names = list(df._data.names)
+            level_names = self._data.level_names
+            multiindex = self._data.multiindex
+            rangeindex = self._data.rangeindex
+        elif isinstance(column_names, (pd.Index, cudf.Index)):
+            if isinstance(column_names, (pd.MultiIndex, cudf.MultiIndex)):
+                multiindex = True
+                if isinstance(column_names, cudf.MultiIndex):
+                    names = list(iter(column_names.to_pandas()))
+                else:
+                    names = list(iter(column_names))
+                rangeindex = False
+            else:
+                multiindex = False
+                names = column_names
+                if isinstance(names, cudf.Index):
+                    names = names.to_pandas()
+                rangeindex = isinstance(
+                    column_names, (pd.RangeIndex, cudf.RangeIndex)
+                )
+            level_names = tuple(column_names.names)
+        else:
+            names = column_names
+            level_names = None
+            multiindex = False
+            rangeindex = False
+
         cols = {
             name: (
                 df._data[name].copy(deep=deep)
@@ -2661,17 +2687,13 @@ def _reindex(
             )
             for name in names
         }
-        if column_names is None:
-            level_names = self._data.level_names
-        elif isinstance(column_names, pd.Index):
-            level_names = tuple(column_names.names)
-        else:
-            level_names = None
+
         result = self.__class__._from_data(
             data=cudf.core.column_accessor.ColumnAccessor(
                 cols,
-                multiindex=self._data.multiindex,
+                multiindex=multiindex,
                 level_names=level_names,
+                rangeindex=rangeindex,
             ),
             index=index,
         )
diff --git a/python/cudf/cudf/tests/test_dataframe.py b/python/cudf/cudf/tests/test_dataframe.py
index 6ddab6ed3f5..ce3c3641a65 100644
--- a/python/cudf/cudf/tests/test_dataframe.py
+++ b/python/cudf/cudf/tests/test_dataframe.py
@@ -3378,6 +3378,51 @@ def test_series_string_reindex(copy):
     )
 
 
+@pytest.mark.parametrize("names", [None, ["a", "b"]])
+@pytest.mark.parametrize("klass", [cudf.MultiIndex, pd.MultiIndex])
+def test_reindex_multiindex_col_to_multiindex(names, klass):
+    idx = pd.Index(
+        [("A", "one"), ("A", "two")],
+        dtype="object",
+    )
+    df = pd.DataFrame([[1, 2]], columns=idx)
+    gdf = cudf.from_pandas(df)
+    midx = klass.from_tuples([("A", "one"), ("A", "three")], names=names)
+    result = gdf.reindex(columns=midx)
+    expected = cudf.DataFrame([[1, None]], columns=midx)
+    # (pandas2.0): check_dtype=False won't be needed
+    # as None col will return object instead of float
+    assert_eq(result, expected, check_dtype=False)
+
+
+@pytest.mark.parametrize("names", [None, ["a", "b"]])
+@pytest.mark.parametrize("klass", [cudf.MultiIndex, pd.MultiIndex])
+def test_reindex_tuple_col_to_multiindex(names, klass):
+    idx = pd.Index(
+        [("A", "one"), ("A", "two")], dtype="object", tupleize_cols=False
+    )
+    df = pd.DataFrame([[1, 2]], columns=idx)
+    gdf = cudf.from_pandas(df)
+    midx = klass.from_tuples([("A", "one"), ("A", "two")], names=names)
+    result = gdf.reindex(columns=midx)
+    expected = cudf.DataFrame([[1, 2]], columns=midx)
+    assert_eq(result, expected)
+
+
+@pytest.mark.parametrize("name", [None, "foo"])
+@pytest.mark.parametrize("klass", [range, cudf.RangeIndex, pd.RangeIndex])
+def test_reindex_columns_rangeindex_keeps_rangeindex(name, klass):
+    new_columns = klass(3)
+    exp_name = None
+    if klass is not range:
+        new_columns.name = name
+        exp_name = name
+    df = cudf.DataFrame([[1, 2]])
+    result = df.reindex(columns=new_columns).columns
+    expected = pd.RangeIndex(3, name=exp_name)
+    assert_eq(result, expected)
+
+
 def test_to_frame(pdf, gdf):
     assert_eq(pdf.x.to_frame(), gdf.x.to_frame())