Вот современный подход, используя pathlib и менеджер контекста. Помещает файлы непосредственно в zip, а не в подпапку.
def zip_dir(filename: str, dir_to_zip: pathlib.Path):
with zipfile.ZipFile(filename, 'w', zipfile.ZIP_DEFLATED) as zipf:
# Use glob instead of iterdir(), to cover all subdirectories.
for directory in dir_to_zip.glob('**'):
for file in directory.iterdir():
if not file.is_file():
continue
# Strip the first component, so we don't create an uneeded subdirectory
# containing everything.
zip_path = pathlib.Path(*file.parts[1:])
# Use a string, since zipfile doesn't support pathlib directly.
zipf.write(str(file), str(zip_path))