diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index 203ea2152886a..067ff32b85862 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -80,8 +80,7 @@ def wrapper(left, right):
     cache=True,
 )
 @inherit_names(
-    ["mean", "freq", "freqstr", "asi8", "_box_values", "_box_func"],
-    DatetimeLikeArrayMixin,
+    ["mean", "freq", "freqstr", "asi8", "_box_func"], DatetimeLikeArrayMixin,
 )
 class DatetimeIndexOpsMixin(ExtensionIndex):
     """
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index d411867af2ef8..ce5008630e53d 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -37,7 +37,7 @@
     pandas_dtype,
 )
 from pandas.core.dtypes.dtypes import ExtensionDtype
-from pandas.core.dtypes.generic import ABCDataFrame
+from pandas.core.dtypes.generic import ABCDataFrame, ABCDatetimeIndex, ABCTimedeltaIndex
 from pandas.core.dtypes.missing import array_equivalent, isna
 
 import pandas.core.algorithms as algos
@@ -653,7 +653,9 @@ def values(self):
             vals = self._get_level_values(i)
             if is_categorical_dtype(vals):
                 vals = vals._internal_get_values()
-            if isinstance(vals.dtype, ExtensionDtype) or hasattr(vals, "_box_values"):
+            if isinstance(vals.dtype, ExtensionDtype) or isinstance(
+                vals, (ABCDatetimeIndex, ABCTimedeltaIndex)
+            ):
                 vals = vals.astype(object)
             vals = np.array(vals, copy=False)
             values.append(vals)