diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index a15da861cfbec..27d8792797e39 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -388,6 +388,7 @@ Categorical
 Datetimelike
 ^^^^^^^^^^^^
 - Bug in :class:`Timestamp` constructor failing to raise when ``tz=None`` is explicitly specified in conjunction with timezone-aware ``tzinfo`` or data (:issue:`48688`)
+- Bug in :func:`Datafreme.drop` returning ``Freq=None`` when the dataframe has a ``DatetimeIndex`` (:issue:`58743`)
 - Bug in :func:`date_range` where the last valid timestamp would sometimes not be produced (:issue:`56134`)
 - Bug in :func:`date_range` where using a negative frequency value would not include all points between the start and end values (:issue:`56382`)
 - Bug in :func:`tseries.api.guess_datetime_format` would fail to infer time format when "%Y" == "%H%M" (:issue:`57452`)
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index 78f04f57029b1..8b05581752ac8 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -48,12 +48,13 @@
 from pandas.core.tools.times import to_time
 
 if TYPE_CHECKING:
-    from collections.abc import Hashable
+    from collections.abc import Hashable, Iterable
 
     from pandas._typing import (
         Dtype,
         DtypeObj,
         Frequency,
+        IgnoreRaise,
         IntervalClosedType,
         Self,
         TimeAmbiguous,
@@ -813,6 +814,18 @@ def indexer_between_time(
 
         return mask.nonzero()[0]
 
+    # --------------------------------------------------------------------
+
+    def drop(
+        self,
+        labels: Index | np.ndarray | Iterable[Hashable],
+        errors: IgnoreRaise = "raise",
+    ) -> DatetimeIndex:
+        if self.freq is not None:
+            return Index.drop(self, labels, errors)._with_freq("infer")  # type: ignore[attr-defined]
+        else:
+            return Index.drop(self, labels, errors)  # type: ignore[return-value]
+
 
 def date_range(
     start=None,
diff --git a/pandas/tests/generic/test_generic.py b/pandas/tests/generic/test_generic.py
index 0b607d91baf65..e2b1426fd62bb 100644
--- a/pandas/tests/generic/test_generic.py
+++ b/pandas/tests/generic/test_generic.py
@@ -483,3 +483,20 @@ def test_flags_identity(self, frame_or_series):
         assert obj.flags is obj.flags
         obj2 = obj.copy()
         assert obj2.flags is not obj.flags
+
+    @pytest.mark.parametrize("freq", ["YE", "ME", "D"])
+    def test_drop_method_freq_preservation(self, freq):
+        # GH 58846
+        start = "1970-01-01"
+        periods = 10
+
+        index = date_range(start=start, periods=periods, freq=freq)
+        df = DataFrame((np.ones(len(index))), index=index)
+
+        # set inplace as false
+        test_df = df.drop(index=df.index[[0, periods - 1]], inplace=False)
+        tm.assert_equal(test_df.index.freq, index.freq)
+
+        # set inplace as true
+        df.drop(index=df.index[[0, periods - 1]], inplace=True)
+        tm.assert_equal(df.index.freq, index.freq)
diff --git a/pandas/tests/indexes/datetimes/methods/test_delete.py b/pandas/tests/indexes/datetimes/methods/test_delete.py
index 2341499977f22..06822d6bc9004 100644
--- a/pandas/tests/indexes/datetimes/methods/test_delete.py
+++ b/pandas/tests/indexes/datetimes/methods/test_delete.py
@@ -132,9 +132,8 @@ def test_delete_slice2(self, tz, unit):
         assert result.freq == expected.freq
         assert result.tz == expected.tz
 
-        # reset freq to None
         result = ts.drop(ts.index[[1, 3, 5, 7, 9]]).index
-        expected = dti[::2]._with_freq(None)
+        expected = dti[::2]
         tm.assert_index_equal(result, expected)
         assert result.name == expected.name
         assert result.freq == expected.freq