diff --git a/Lib/concurrent/futures/process.py b/Lib/concurrent/futures/process.py
index 8e9b69a8f08b42..7d62019996ac83 100644
--- a/Lib/concurrent/futures/process.py
+++ b/Lib/concurrent/futures/process.py
@@ -46,6 +46,7 @@
 __author__ = 'Brian Quinlan (brian@sweetapp.com)'
 
 import atexit
+import contextlib
 import os
 from concurrent.futures import _base
 import queue
@@ -68,19 +69,41 @@ class _ThreadWakeup:
     def __init__(self):
         self._closed = False
         self._reader, self._writer = mp.Pipe(duplex=False)
+        # bpo-39995: Event used to ensure that the pipe is not closed while
+        # sending or receiving bytes. Initialize event as True.
+        self._close_event = threading.Event()
+        self._close_event.set()
 
     def close(self):
-        if not self._closed:
-            self._closed = True
-            self._writer.close()
-            self._reader.close()
+        if self._closed:
+            return
+
+        self._close_event.wait()
+
+        self._closed = True
+        self._writer.close()
+        self._reader.close()
+
+    @contextlib.contextmanager
+    def _block_close(self):
+        self._close_event.clear()
+        # If close() is called from a different thread,
+        # it blocks until the close event is set again.
+        try:
+            yield
+        finally:
+            self._close_event.set()
 
     def wakeup(self):
-        if not self._closed:
+        with self._block_close():
+            if self._closed:
+                return
             self._writer.send_bytes(b"")
 
     def clear(self):
-        if not self._closed:
+        with self._block_close():
+            if self._closed:
+                return
             while self._reader.poll():
                 self._reader.recv_bytes()
 
diff --git a/Misc/NEWS.d/next/Library/2020-04-28-17-57-47.bpo-39995.4cGpi8.rst b/Misc/NEWS.d/next/Library/2020-04-28-17-57-47.bpo-39995.4cGpi8.rst
new file mode 100644
index 00000000000000..4e4a87939e2edc
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-04-28-17-57-47.bpo-39995.4cGpi8.rst
@@ -0,0 +1,3 @@
+Fix a race condition in concurrent.futures._ThreadWakeup: it now uses an
+internal threading event to ensure that the pipe is not closed while sending or
+receiving bytes. Patch by Kyle Stanley and Victor Stinner.