diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index 8ee2baf0768ec..5e8677e2ae7a6 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -127,6 +127,8 @@ Other API changes
 - Passing ``dtype`` of "timedelta64[s]", "timedelta64[ms]", or "timedelta64[us]" to :class:`TimedeltaIndex`, :class:`Series`, or :class:`DataFrame` constructors will now retain that dtype instead of casting to "timedelta64[ns]"; passing a dtype with lower resolution for :class:`Series` or :class:`DataFrame` will be cast to the lowest supported resolution "timedelta64[s]" (:issue:`49014`)
 - Passing a ``np.datetime64`` object with non-nanosecond resolution to :class:`Timestamp` will retain the input resolution if it is "s", "ms", or "ns"; otherwise it will be cast to the closest supported resolution (:issue:`49008`)
 - The ``other`` argument in :meth:`DataFrame.mask` and :meth:`Series.mask` now defaults to ``no_default`` instead of ``np.nan`` consistent with :meth:`DataFrame.where` and :meth:`Series.where`. Entries will be filled with the corresponding NULL value (``np.nan`` for numpy dtypes, ``pd.NA`` for extension dtypes). (:issue:`49111`)
+- When creating a :class:`Series` with a object-dtype :class:`Index` of datetime objects, pandas no longer silently converts the index to a :class:`DatetimeIndex` (:issue:`39307`, :issue:`23598`)
+-
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_200.deprecations:
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 388c9223074a0..4f3c908817ac7 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -825,7 +825,12 @@ def _set_axis_nocheck(self, labels, axis: Axis, inplace: bool_t, copy: bool_t):
             setattr(obj, obj._get_axis_name(axis), labels)
             return obj
 
+    @final
     def _set_axis(self, axis: AxisInt, labels: AnyArrayLike | list) -> None:
+        """
+        This is called from the cython code when we set the `index` attribute
+        directly, e.g. `series.index = [1, 2, 3]`.
+        """
         labels = ensure_index(labels)
         self._mgr.set_axis(axis, labels)
         self._clear_item_cache()
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 558d879127410..6620cc1786340 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -29,7 +29,6 @@
     lib,
     properties,
     reshape,
-    tslibs,
 )
 from pandas._libs.lib import no_default
 from pandas._typing import (
@@ -132,13 +131,11 @@
 )
 from pandas.core.indexes.accessors import CombinedDatetimelikeProperties
 from pandas.core.indexes.api import (
-    CategoricalIndex,
     DatetimeIndex,
     Float64Index,
     Index,
     MultiIndex,
     PeriodIndex,
-    TimedeltaIndex,
     default_index,
     ensure_index,
 )
@@ -570,36 +567,6 @@ def _constructor_expanddim(self) -> Callable[..., DataFrame]:
     def _can_hold_na(self) -> bool:
         return self._mgr._can_hold_na
 
-    def _set_axis(self, axis: AxisInt, labels: AnyArrayLike | list) -> None:
-        """
-        Override generic, we want to set the _typ here.
-
-        This is called from the cython code when we set the `index` attribute
-        directly, e.g. `series.index = [1, 2, 3]`.
-        """
-        labels = ensure_index(labels)
-
-        if labels._is_all_dates and not (
-            type(labels) is Index and not isinstance(labels.dtype, np.dtype)
-        ):
-            # exclude e.g. timestamp[ns][pyarrow] dtype from this casting
-            deep_labels = labels
-            if isinstance(labels, CategoricalIndex):
-                deep_labels = labels.categories
-
-            if not isinstance(
-                deep_labels, (DatetimeIndex, PeriodIndex, TimedeltaIndex)
-            ):
-                try:
-                    labels = DatetimeIndex(labels)
-                except (tslibs.OutOfBoundsDatetime, ValueError):
-                    # labels may exceeds datetime bounds,
-                    # or not be a DatetimeIndex
-                    pass
-
-        # The ensure_index call above ensures we have an Index object
-        self._mgr.set_axis(axis, labels)
-
     # ndarray compatibility
     @property
     def dtype(self) -> DtypeObj:
diff --git a/pandas/io/pytables.py b/pandas/io/pytables.py
index edd6c3bd9d1e5..a95d1b9d7cce6 100644
--- a/pandas/io/pytables.py
+++ b/pandas/io/pytables.py
@@ -3006,7 +3006,7 @@ def read_index_node(
         attrs = node._v_attrs
         factory, kwargs = self._get_index_factory(attrs)
 
-        if kind == "date":
+        if kind == "date" or kind == "object":
             index = factory(
                 _unconvert_index(
                     data, kind, encoding=self.encoding, errors=self.errors
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index d05eccae922aa..208917ca34b04 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -1986,7 +1986,9 @@ def test_series_constructor_datetimelike_index_coercion(self):
         ser = Series(np.random.randn(len(idx)), idx.astype(object))
         with tm.assert_produces_warning(FutureWarning):
             assert ser.index.is_all_dates
-        assert isinstance(ser.index, DatetimeIndex)
+        # as of 2.0, we no longer silently cast the object-dtype index
+        #  to DatetimeIndex GH#39307, GH#23598
+        assert not isinstance(ser.index, DatetimeIndex)
 
     def test_series_constructor_infer_multiindex(self):
         index_lists = [["a", "a", "b", "b"], ["x", "y", "x", "y"]]