diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 28f7df98cb86b..d56f3c978384c 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -562,6 +562,8 @@ Strings
 
 Interval
 ^^^^^^^^
+
+- Bug in :meth:`DataFrame.replace` and :meth:`Series.replace` where :class:`Interval` dtypes would be converted to object dtypes (:issue:`34871`)
 - Bug in :meth:`IntervalIndex.take` with negative indices and ``fill_value=None`` (:issue:`37330`)
 -
 -
@@ -626,6 +628,11 @@ I/O
 - :meth:`to_excel` and :meth:`to_markdown` support writing to fsspec URLs such as S3 and Google Cloud Storage (:issue:`33987`)
 - Bug in :meth:`read_fw` was not skipping blank lines (even with ``skip_blank_lines=True``) (:issue:`37758`)
 
+Period
+^^^^^^
+
+- Bug in :meth:`DataFrame.replace` and :meth:`Series.replace` where :class:`Period` dtypes would be converted to object dtypes (:issue:`34871`)
+
 Plotting
 ^^^^^^^^
 
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index 967e218078a28..f1759fbda0b8c 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -2041,6 +2041,16 @@ class ObjectValuesExtensionBlock(ExtensionBlock):
     def external_values(self):
         return self.values.astype(object)
 
+    def _can_hold_element(self, element: Any) -> bool:
+        if is_valid_nat_for_dtype(element, self.dtype):
+            return True
+        if isinstance(element, list) and len(element) == 0:
+            return True
+        tipo = maybe_infer_dtype_type(element)
+        if tipo is not None:
+            return issubclass(tipo.type, self.dtype.type)
+        return isinstance(element, self.dtype.type)
+
 
 class NumericBlock(Block):
     __slots__ = ()
diff --git a/pandas/tests/frame/methods/test_replace.py b/pandas/tests/frame/methods/test_replace.py
index 8f3dcc96ddc3d..8e59dd959ab57 100644
--- a/pandas/tests/frame/methods/test_replace.py
+++ b/pandas/tests/frame/methods/test_replace.py
@@ -1523,12 +1523,10 @@ def test_replace_with_duplicate_columns(self, replacement):
 
         tm.assert_frame_equal(result, expected)
 
-    def test_replace_period_ignore_float(self, frame_or_series):
-        """
-        Regression test for GH#34871: if df.replace(1.0, 0.0) is called on a df
-        with a Period column the old, faulty behavior is to raise TypeError.
-        """
-        obj = DataFrame({"Per": [pd.Period("2020-01")] * 3})
+    @pytest.mark.parametrize("value", [pd.Period("2020-01"), pd.Interval(0, 5)])
+    def test_replace_ea_ignore_float(self, frame_or_series, value):
+        # GH#34871
+        obj = DataFrame({"Per": [value] * 3})
         if frame_or_series is not DataFrame:
             obj = obj["Per"]