diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index e7f6b911f2fb1..0b546bed1c2b7 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -1398,7 +1398,7 @@ def _to_datetimearray(self) -> DatetimeArray:
         np_dtype = np.dtype(f"M8[{pa_type.unit}]")
         dtype = tz_to_dtype(pa_type.tz, pa_type.unit)
         np_array = self._pa_array.to_numpy()
-        np_array = np_array.astype(np_dtype)
+        np_array = np_array.astype(np_dtype, copy=False)
         return DatetimeArray._simple_new(np_array, dtype=dtype)
 
     def _to_timedeltaarray(self) -> TimedeltaArray:
@@ -1409,7 +1409,7 @@ def _to_timedeltaarray(self) -> TimedeltaArray:
         assert pa.types.is_duration(pa_type)
         np_dtype = np.dtype(f"m8[{pa_type.unit}]")
         np_array = self._pa_array.to_numpy()
-        np_array = np_array.astype(np_dtype)
+        np_array = np_array.astype(np_dtype, copy=False)
         return TimedeltaArray._simple_new(np_array, dtype=np_dtype)
 
     def _values_for_json(self) -> np.ndarray: