diff --git a/django/core/files/storage.py b/django/core/files/storage.py
index c1e654beeb..b9f3e01f0d 100644
--- a/django/core/files/storage.py
+++ b/django/core/files/storage.py
@@ -215,6 +215,7 @@ class FileSystemStorage(Storage):
                                 _file = os.fdopen(fd, mode)
                             _file.write(chunk)
                     finally:
+                        content.close()
                         locks.unlock(fd)
                         if _file is not None:
                             _file.close()