diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index d0a31b68250ad..e78714487f01e 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -163,7 +163,7 @@ def __new__(
                 "represent unambiguous timedelta values durations."
             )
 
-        if isinstance(data, TimedeltaArray):
+        if isinstance(data, TimedeltaArray) and freq is None:
             if copy:
                 data = data.copy()
             return cls._simple_new(data, name=name, freq=freq)
diff --git a/pandas/tests/indexes/timedeltas/test_constructors.py b/pandas/tests/indexes/timedeltas/test_constructors.py
index 39abbf59d1e56..32e6821e87f05 100644
--- a/pandas/tests/indexes/timedeltas/test_constructors.py
+++ b/pandas/tests/indexes/timedeltas/test_constructors.py
@@ -47,6 +47,12 @@ def test_infer_from_tdi_mismatch(self):
             # GH#23789
             TimedeltaArray(tdi, freq="D")
 
+        with pytest.raises(ValueError, match=msg):
+            TimedeltaIndex(tdi._data, freq="D")
+
+        with pytest.raises(ValueError, match=msg):
+            TimedeltaArray(tdi._data, freq="D")
+
     def test_dt64_data_invalid(self):
         # GH#23539
         # passing tz-aware DatetimeIndex raises, naive or ndarray[datetime64]