diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index ee9b948a76ac8..5f204a8c18368 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -486,8 +486,8 @@ def snap(self, freq="S"):
                     s = t1
             snapped[i] = s
 
-        # we know it conforms; skip check
-        return DatetimeIndex._simple_new(snapped, name=self.name, tz=self.tz, freq=freq)
+        dta = DatetimeArray(snapped, dtype=self.dtype)
+        return DatetimeIndex._simple_new(dta, name=self.name)
 
     def _parsed_string_to_bounds(self, reso, parsed):
         """
diff --git a/pandas/tests/indexes/datetimes/test_snap.py b/pandas/tests/indexes/datetimes/test_snap.py
index a21d27d23f6b5..8baea9fe8341f 100644
--- a/pandas/tests/indexes/datetimes/test_snap.py
+++ b/pandas/tests/indexes/datetimes/test_snap.py
@@ -28,6 +28,8 @@ def test_dti_snap(name, tz):
     expected = expected.repeat([3, 4])
     tm.assert_index_equal(result, expected)
     assert result.tz == expected.tz
+    assert result.freq is None
+    assert expected.freq is None
 
     result = dti.snap(freq="B")
 
@@ -35,3 +37,5 @@ def test_dti_snap(name, tz):
     expected = expected.repeat([1, 1, 1, 2, 2])
     tm.assert_index_equal(result, expected)
     assert result.tz == expected.tz
+    assert result.freq is None
+    assert expected.freq is None