diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index c5cfa4c2d1fcd..86f2793341d76 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -1,6 +1,9 @@
 from __future__ import annotations
 
-from datetime import datetime
+from datetime import (
+    date,
+    datetime,
+)
 import functools
 from itertools import zip_longest
 import operator
@@ -764,7 +767,11 @@ def _shallow_copy(self: _IndexT, values, name: Hashable = no_default) -> _IndexT
         name : Label, defaults to self.name
         """
         name = self._name if name is no_default else name
+        u = self._simple_new(values, name=name)
+        if all(isinstance(x, date) for x in u):
+            from pandas import to_datetime
 
+            return to_datetime(u)
         return self._simple_new(values, name=name)
 
     def _view(self: _IndexT) -> _IndexT:
diff --git a/pandas/tests/series/methods/test_reset_index.py b/pandas/tests/series/methods/test_reset_index.py
index b159317bf813b..90bee53a860b8 100644
--- a/pandas/tests/series/methods/test_reset_index.py
+++ b/pandas/tests/series/methods/test_reset_index.py
@@ -1,4 +1,7 @@
-from datetime import datetime
+from datetime import (
+    date,
+    datetime,
+)
 
 import numpy as np
 import pytest
@@ -179,3 +182,23 @@ def test_reset_index_dtypes_on_empty_series_with_multiindex(array, dtype):
         {"level_0": np.int64, "level_1": np.float64, "level_2": dtype, 0: object}
     )
     tm.assert_series_equal(result, expected)
+
+
+def test_set_index_MultiIndex():
+    df = DataFrame(
+        {
+            "date": [date(2021, 8, 1), date(2021, 8, 2), date(2021, 8, 3)],
+            "ticker": ["aapl", "goog", "yhoo"],
+            "value": [5.63269, 4.45609, 2.74843],
+        }
+    )
+
+    df.set_index(["date", "ticker"], inplace=True)
+    res = df.index.get_level_values(0)
+    ex = pd.DatetimeIndex(
+        ["2021-08-01", "2021-08-02", "2021-08-03"],
+        dtype="datetime64[ns]",
+        name="date",
+        freq=None,
+    )
+    tm.assert_index_equal(ex, res)