diff --git a/python/cudf/cudf/core/multiindex.py b/python/cudf/cudf/core/multiindex.py
index 7c132e3fb71..8c4f87d5f67 100644
--- a/python/cudf/cudf/core/multiindex.py
+++ b/python/cudf/cudf/core/multiindex.py
@@ -1422,15 +1422,21 @@ def _clean_nulls_from_index(self):
         )
 
     def memory_usage(self, deep=False):
+        if deep:
+            warnings.warn(
+                "The deep parameter is ignored and is only included "
+                "for pandas compatibility."
+            )
+
         n = 0
-        for col in self._data._columns:
-            n += col._memory_usage(deep=deep)
-        if self._levels:
-            for level in self._levels:
+        for col in self._data.columns:
+            n += col.memory_usage()
+        if self.levels:
+            for level in self.levels:
                 n += level.memory_usage(deep=deep)
-        if self._codes:
-            for col in self._codes._columns:
-                n += col._memory_usage(deep=deep)
+        if self.codes:
+            for col in self.codes._data.columns:
+                n += col.memory_usage()
         return n
 
     def difference(self, other, sort=None):
diff --git a/python/cudf/cudf/tests/test_dataframe.py b/python/cudf/cudf/tests/test_dataframe.py
index 8fac730fe54..d07caef11d5 100644
--- a/python/cudf/cudf/tests/test_dataframe.py
+++ b/python/cudf/cudf/tests/test_dataframe.py
@@ -5406,9 +5406,8 @@ def test_memory_usage_list():
     assert expected == df.A.memory_usage()
 
 
-@pytest.mark.xfail
-def test_memory_usage_multi():
-    rows = int(100)
+@pytest.mark.parametrize("rows", [10, 100])
+def test_memory_usage_multi(rows):
     deep = True
     df = pd.DataFrame(
         {
@@ -5418,7 +5417,6 @@ def test_memory_usage_multi():
         }
     ).set_index(["B", "C"])
     gdf = cudf.from_pandas(df)
-
     # Assume MultiIndex memory footprint is just that
     # of the underlying columns, levels, and codes
     expect = rows * 16  # Source Columns