diff --git a/doc/source/whatsnew/v2.2.0.rst b/doc/source/whatsnew/v2.2.0.rst
index 919ac8b03f936..b7f4bd014bf0a 100644
--- a/doc/source/whatsnew/v2.2.0.rst
+++ b/doc/source/whatsnew/v2.2.0.rst
@@ -455,6 +455,7 @@ Other Deprecations
 - Deprecated allowing non-keyword arguments in :meth:`DataFrame.to_xml` except ``path_or_buffer``. (:issue:`54229`)
 - Deprecated allowing passing :class:`BlockManager` objects to :class:`DataFrame` or :class:`SingleBlockManager` objects to :class:`Series` (:issue:`52419`)
 - Deprecated downcasting behavior in :meth:`Series.where`, :meth:`DataFrame.where`, :meth:`Series.mask`, :meth:`DataFrame.mask`, :meth:`Series.clip`, :meth:`DataFrame.clip`; in a future version these will not infer object-dtype columns to non-object dtype, or all-round floats to integer dtype. Call ``result.infer_objects(copy=False)`` on the result for object inference, or explicitly cast floats to ints. To opt in to the future version, use ``pd.set_option("future.no_silent_downcasting", True)`` (:issue:`53656`)
+- Deprecated dtype inference when setting a :class:`Index` into a :class:`DataFrame`, cast explicitly instead (:issue:`56102`)
 - Deprecated including the groups in computations when using :meth:`.DataFrameGroupBy.apply` and :meth:`.DataFrameGroupBy.resample`; pass ``include_groups=False`` to exclude the groups (:issue:`7155`)
 - Deprecated indexing an :class:`Index`  with a boolean indexer of length zero (:issue:`55820`)
 - Deprecated not passing a tuple to :class:`.DataFrameGroupBy.get_group` or :class:`.SeriesGroupBy.get_group` when grouping by a length-1 list-like (:issue:`25971`)
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 179279cc08bab..ba350c81ee7c9 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -5219,7 +5219,21 @@ def _sanitize_column(self, value) -> tuple[ArrayLike, BlockValuesRefs | None]:
 
         if is_list_like(value):
             com.require_length_match(value, self.index)
-        return sanitize_array(value, self.index, copy=True, allow_2d=True), None
+        arr = sanitize_array(value, self.index, copy=True, allow_2d=True)
+        if (
+            isinstance(value, Index)
+            and value.dtype == "object"
+            and arr.dtype != value.dtype
+        ):  #
+            # TODO: Remove kludge in sanitize_array for string mode when enforcing
+            # this deprecation
+            warnings.warn(
+                "Setting an Index with object dtype into a DataFrame will no longer "
+                "infer another dtype. Cast the Index explicitly before setting.",
+                FutureWarning,
+                stacklevel=find_stack_level(),
+            )
+        return arr, None
 
     @property
     def _series(self):
diff --git a/pandas/tests/frame/indexing/test_setitem.py b/pandas/tests/frame/indexing/test_setitem.py
index c0ba2f245efed..856bda9dddcd7 100644
--- a/pandas/tests/frame/indexing/test_setitem.py
+++ b/pandas/tests/frame/indexing/test_setitem.py
@@ -786,6 +786,24 @@ def test_loc_setitem_ea_dtype(self):
         df.iloc[:, 0] = Series([11], dtype="Int64")
         tm.assert_frame_equal(df, expected)
 
+    def test_setitem_object_inferring(self):
+        # GH#56102
+        idx = Index([Timestamp("2019-12-31")], dtype=object)
+        df = DataFrame({"a": [1]})
+        with tm.assert_produces_warning(FutureWarning, match="infer"):
+            df.loc[:, "b"] = idx
+        with tm.assert_produces_warning(FutureWarning, match="infer"):
+            df["c"] = idx
+
+        expected = DataFrame(
+            {
+                "a": [1],
+                "b": Series([Timestamp("2019-12-31")], dtype="datetime64[ns]"),
+                "c": Series([Timestamp("2019-12-31")], dtype="datetime64[ns]"),
+            }
+        )
+        tm.assert_frame_equal(df, expected)
+
 
 class TestSetitemTZAwareValues:
     @pytest.fixture