diff --git a/python/cudf/cudf/core/indexed_frame.py b/python/cudf/cudf/core/indexed_frame.py
index 394904c5855..b4a689804c7 100644
--- a/python/cudf/cudf/core/indexed_frame.py
+++ b/python/cudf/cudf/core/indexed_frame.py
@@ -644,7 +644,11 @@ def index(self, value):
                 f"Length mismatch: Expected axis has {old_length} elements, "
                 f"new values have {len(value)} elements"
             )
-        self._index = Index(value)
+        # avoid unnecessary cast to Index
+        if not isinstance(value, BaseIndex):
+            value = Index(value)
+
+        self._index = value
 
     @_cudf_nvtx_annotate
     def replace(
diff --git a/python/cudf/cudf/tests/test_index.py b/python/cudf/cudf/tests/test_index.py
index 8e7532d044d..b92ae1b3364 100644
--- a/python/cudf/cudf/tests/test_index.py
+++ b/python/cudf/cudf/tests/test_index.py
@@ -3266,3 +3266,17 @@ def test_index_datetime_repeat():
     actual = gidx.to_frame().repeat(5)
 
     assert_eq(actual.index, expected)
+
+
+@pytest.mark.parametrize(
+    "index",
+    [
+        cudf.Index([1]),
+        cudf.RangeIndex(1),
+        cudf.MultiIndex(levels=[[0]], codes=[[0]]),
+    ],
+)
+def test_index_assignment_no_shallow_copy(index):
+    df = cudf.DataFrame(range(1))
+    df.index = index
+    assert df.index is index