diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index 197cdc3f436a1..bdcd8f1ef0d50 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -37,6 +37,7 @@
     pa_version_under8p0,
     pa_version_under9p0,
     pa_version_under11p0,
+    pa_version_under13p0,
 )
 
 from pandas.core.dtypes.dtypes import (
@@ -1005,7 +1006,14 @@ def _patch_combine(self, obj, other, op):
 
     def _is_temporal_supported(self, opname, pa_dtype):
         return not pa_version_under8p0 and (
-            opname in ("__add__", "__radd__")
+            (
+                opname in ("__add__", "__radd__")
+                or (
+                    opname
+                    in ("__truediv__", "__rtruediv__", "__floordiv__", "__rfloordiv__")
+                    and not pa_version_under13p0
+                )
+            )
             and pa.types.is_duration(pa_dtype)
             or opname in ("__sub__", "__rsub__")
             and pa.types.is_temporal(pa_dtype)
@@ -1054,7 +1062,14 @@ def _get_arith_xfail_marker(self, opname, pa_dtype):
                     f"for {pa_dtype}"
                 )
             )
-        elif arrow_temporal_supported and pa.types.is_time(pa_dtype):
+        elif arrow_temporal_supported and (
+            pa.types.is_time(pa_dtype)
+            or (
+                opname
+                in ("__truediv__", "__rtruediv__", "__floordiv__", "__rfloordiv__")
+                and pa.types.is_duration(pa_dtype)
+            )
+        ):
             mark = pytest.mark.xfail(
                 raises=TypeError,
                 reason=(