diff --git a/doc/source/whatsnew/v1.3.3.rst b/doc/source/whatsnew/v1.3.3.rst
index 3dee3aa5e7c7a..9aac0a9ad9681 100644
--- a/doc/source/whatsnew/v1.3.3.rst
+++ b/doc/source/whatsnew/v1.3.3.rst
@@ -17,7 +17,7 @@ Fixed regressions
 - Fixed regression in :class:`DataFrame` constructor failing to broadcast for defined :class:`Index` and len one list of :class:`Timestamp` (:issue:`42810`)
 - Performance regression in :meth:`core.window.ewm.ExponentialMovingWindow.mean` (:issue:`42333`)
 - Fixed regression in :meth:`.GroupBy.agg` incorrectly raising in some cases (:issue:`42390`)
--
+- Fixed regression in :meth:`RangeIndex.where` and :meth:`RangeIndex.putmask` raising ``AssertionError`` when result did not represent a :class:`RangeIndex` (:issue:`43240`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 2615bfffb3cd9..41355b9a44b85 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -4890,8 +4890,7 @@ def putmask(self, mask, value) -> Index:
             values, mask.sum(), converted  # type: ignore[arg-type]
         )
         np.putmask(values, mask, converted)
-
-        return type(self)._simple_new(values, name=self.name)
+        return self._shallow_copy(values)
 
     def equals(self, other: Any) -> bool:
         """
diff --git a/pandas/tests/indexes/ranges/test_setops.py b/pandas/tests/indexes/ranges/test_setops.py
index ba938f82e9d89..210bcd300b1b0 100644
--- a/pandas/tests/indexes/ranges/test_setops.py
+++ b/pandas/tests/indexes/ranges/test_setops.py
@@ -354,3 +354,17 @@ def test_symmetric_difference(self):
         result = left.symmetric_difference(right[1:])
         expected = Int64Index([1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14])
         tm.assert_index_equal(result, expected)
+
+    def test_putmask_range_cast(self):
+        # GH#43240
+        idx = RangeIndex(0, 5, name="test")
+        result = idx.putmask(np.array([True, True, False, False, False]), 10)
+        expected = Index([10, 10, 2, 3, 4], name="test")
+        tm.assert_index_equal(result, expected)
+
+    def test_where_range_cast(self):
+        # GH#43240
+        idx = RangeIndex(0, 5, name="test")
+        result = idx.where(np.array([False, False, True, True, True]), 10)
+        expected = Index([10, 10, 2, 3, 4], name="test")
+        tm.assert_index_equal(result, expected)