diff --git a/pandas/_testing/contexts.py b/pandas/_testing/contexts.py
index eb6e4a917889a..48616ee134582 100644
--- a/pandas/_testing/contexts.py
+++ b/pandas/_testing/contexts.py
@@ -78,14 +78,15 @@ def set_timezone(tz: str) -> Generator[None, None, None]:
     import time
 
     def setTZ(tz) -> None:
-        if tz is None:
-            try:
-                del os.environ["TZ"]
-            except KeyError:
-                pass
-        else:
-            os.environ["TZ"] = tz
-            time.tzset()
+        if hasattr(time, "tzset"):
+            if tz is None:
+                try:
+                    del os.environ["TZ"]
+                except KeyError:
+                    pass
+            else:
+                os.environ["TZ"] = tz
+                time.tzset()
 
     orig_tz = os.environ.get("TZ")
     setTZ(tz)
diff --git a/pandas/tests/tslibs/test_parsing.py b/pandas/tests/tslibs/test_parsing.py
index d8f23156bd4d4..fb05a57056a83 100644
--- a/pandas/tests/tslibs/test_parsing.py
+++ b/pandas/tests/tslibs/test_parsing.py
@@ -17,6 +17,7 @@
 from pandas._libs.tslibs.parsing import parse_datetime_string_with_reso
 from pandas.compat import (
     ISMUSL,
+    is_platform_arm,
     is_platform_windows,
 )
 import pandas.util._test_decorators as td
@@ -26,7 +27,7 @@
 
 
 @pytest.mark.skipif(
-    is_platform_windows() or ISMUSL,
+    is_platform_windows() or ISMUSL or is_platform_arm(),
     reason="TZ setting incorrect on Windows and MUSL Linux",
 )
 def test_parsing_tzlocal_deprecated():