diff --git a/python/pyarrow/util.py b/python/pyarrow/util.py
index 5878d1f90262..a95826e1c005 100644
--- a/python/pyarrow/util.py
+++ b/python/pyarrow/util.py
@@ -231,8 +231,9 @@ def _break_traceback_cycle_from_frame(frame):
 
 
 def _download_urllib(url, out_path):
-    from urllib.request import urlopen
-    with urlopen(url) as response:
+    from urllib.request import urlopen, Request
+    req = Request(url, headers={'User-Agent': 'pyarrow'})
+    with urlopen(req) as response:
         with open(out_path, 'wb') as f:
             f.write(response.read())
 
@@ -264,11 +265,13 @@ def download_tzdata_on_windows():
     # Try to download the files with requests and then fall back to urllib. This
     # works around possible issues in certain older environment (GH-45295)
     try:
-        _download_requests(tzdata_url, tzdata_compressed_path)
-        _download_requests(windows_zones_url, windows_zones_path)
+        import requests  # noqa: F401
+        download_fn = _download_requests
     except ImportError:
-        _download_urllib(tzdata_url, tzdata_compressed_path)
-        _download_urllib(windows_zones_url, windows_zones_path)
+        download_fn = _download_urllib
+
+    download_fn(tzdata_url, tzdata_compressed_path)
+    download_fn(windows_zones_url, windows_zones_path)
 
     assert os.path.exists(tzdata_compressed_path)
     assert os.path.exists(windows_zones_path)