diff --git a/Lib/test/test_concurrent_futures.py b/Lib/test/test_concurrent_futures.py
index c782d4c6e88..ff9a4938034 100644
--- a/Lib/test/test_concurrent_futures.py
+++ b/Lib/test/test_concurrent_futures.py
@@ -1309,6 +1309,9 @@ def tearDownModule():
 
     # cleanup multiprocessing
     multiprocessing.process._cleanup()
+    # Stop the ForkServer process if it's running
+    from multiprocessing import forkserver
+    forkserver._forkserver._stop()
     # bpo-37421: Explicitly call _run_finalizers() to remove immediately
     # temporary directories created by multiprocessing.util.get_temp_dir().
     multiprocessing.util._run_finalizers()
diff --git a/Misc/NEWS.d/next/Tests/2019-07-08-10-11-36.bpo-37421.OY77go.rst b/Misc/NEWS.d/next/Tests/2019-07-08-10-11-36.bpo-37421.OY77go.rst
new file mode 100644
index 00000000000..0766d70f6ed
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2019-07-08-10-11-36.bpo-37421.OY77go.rst
@@ -0,0 +1,2 @@
+test_concurrent_futures now explicitly stops the ForkServer instance if it's
+running.