diff --git a/src/datasets/download/download_manager.py b/src/datasets/download/download_manager.py
index ef06e6a7fe3..d3d89255d13 100644
--- a/src/datasets/download/download_manager.py
+++ b/src/datasets/download/download_manager.py
@@ -130,11 +130,11 @@ def _iter_from_paths(cls, urlpaths: Union[str, List[str]]) -> Generator[str, Non
                 for dirpath, dirnames, filenames in os.walk(urlpath):
                     # skipping hidden directories; prune the search
                     # [:] for the in-place list modification required by os.walk
-                    dirnames[:] = [dirname for dirname in dirnames if not dirname.startswith((".", "__"))]
+                    dirnames[:] = sorted([dirname for dirname in dirnames if not dirname.startswith((".", "__"))])
                     if os.path.basename(dirpath).startswith((".", "__")):
                         # skipping hidden directories
                         continue
-                    for filename in filenames:
+                    for filename in sorted(filenames):
                         if filename.startswith((".", "__")):
                             # skipping hidden files
                             continue
diff --git a/src/datasets/download/mock_download_manager.py b/src/datasets/download/mock_download_manager.py
index 46ac34076e4..84321e708d5 100644
--- a/src/datasets/download/mock_download_manager.py
+++ b/src/datasets/download/mock_download_manager.py
@@ -236,10 +236,11 @@ def iter_files(self, paths):
                     return
                 yield path
             else:
-                for dirpath, _, filenames in os.walk(path):
+                for dirpath, dirnames, filenames in os.walk(path):
                     if os.path.basename(dirpath).startswith((".", "__")):
                         continue
-                    for filename in filenames:
+                    dirnames.sort()
+                    for filename in sorted(filenames):
                         if filename.startswith((".", "__")):
                             continue
                         yield os.path.join(dirpath, filename)
diff --git a/src/datasets/download/streaming_download_manager.py b/src/datasets/download/streaming_download_manager.py
index 42edd42ce85..37d7b732e65 100644
--- a/src/datasets/download/streaming_download_manager.py
+++ b/src/datasets/download/streaming_download_manager.py
@@ -835,11 +835,11 @@ def _iter_from_urlpaths(
                     # skipping hidden directories; prune the search
                     # [:] for the in-place list modification required by os.walk
                     # (only works for local paths as fsspec's walk doesn't support the in-place modification)
-                    dirnames[:] = [dirname for dirname in dirnames if not dirname.startswith((".", "__"))]
+                    dirnames[:] = sorted([dirname for dirname in dirnames if not dirname.startswith((".", "__"))])
                     if xbasename(dirpath).startswith((".", "__")):
                         # skipping hidden directories
                         continue
-                    for filename in filenames:
+                    for filename in sorted(filenames):
                         if filename.startswith((".", "__")):
                             # skipping hidden files
                             continue
diff --git a/tests/test_download_manager.py b/tests/test_download_manager.py
index 695884cd0f7..0dfc0a2098e 100644
--- a/tests/test_download_manager.py
+++ b/tests/test_download_manager.py
@@ -141,5 +141,5 @@ def test_iter_archive_file(tar_nested_jsonl_path):
 def test_iter_files(data_dir_with_hidden_files):
     dl_manager = DownloadManager()
     for num_file, file in enumerate(dl_manager.iter_files(data_dir_with_hidden_files), start=1):
-        pass
+        assert os.path.basename(file) == ("test.txt" if num_file == 1 else "train.txt")
     assert num_file == 2
diff --git a/tests/test_streaming_download_manager.py b/tests/test_streaming_download_manager.py
index 7452e5dacf6..34a5b45e4b0 100644
--- a/tests/test_streaming_download_manager.py
+++ b/tests/test_streaming_download_manager.py
@@ -834,5 +834,5 @@ def test_iter_archive_file(tar_nested_jsonl_path):
 def test_iter_files(data_dir_with_hidden_files):
     dl_manager = StreamingDownloadManager()
     for num_file, file in enumerate(dl_manager.iter_files(data_dir_with_hidden_files), start=1):
-        pass
+        assert os.path.basename(file) == ("test.txt" if num_file == 1 else "train.txt")
     assert num_file == 2