diff --git a/cibuildwheel/docker_container.py b/cibuildwheel/docker_container.py
index bc313a7de..8ee8e5739 100644
--- a/cibuildwheel/docker_container.py
+++ b/cibuildwheel/docker_container.py
@@ -122,7 +122,7 @@ def copy_into(self, from_path: Path, to_path: PurePath) -> None:
         if from_path.is_dir():
             self.call(["mkdir", "-p", to_path])
             subprocess.run(
-                f"tar cf - . | docker exec -i {self.name} tar -xC {shell_quote(to_path)} -f -",
+                f"tar cf - . | docker exec -i {self.name} tar --no-same-owner -xC {shell_quote(to_path)} -f -",
                 shell=True,
                 check=True,
                 cwd=from_path,