diff --git a/prometheus_client/core.py b/prometheus_client/core.py
index 02dc8ae7..e7ab8344 100644
--- a/prometheus_client/core.py
+++ b/prometheus_client/core.py
@@ -426,6 +426,8 @@ def write_value(self, key, value):
 
     def close(self):
         if self._f:
+            self._m.close()
+            self._m = None
             self._f.close()
             self._f = None