diff --git a/Lib/multiprocessing/heap.py b/Lib/multiprocessing/heap.py
index 333b3baf20f..44d9638ff6e 100644
--- a/Lib/multiprocessing/heap.py
+++ b/Lib/multiprocessing/heap.py
@@ -71,7 +71,14 @@ else:
                 os.unlink(name)
                 util.Finalize(self, os.close, (self.fd,))
                 with open(self.fd, 'wb', closefd=False) as f:
-                    f.write(b'\0'*size)
+                    bs = 1024 * 1024
+                    if size >= bs:
+                        zeros = b'\0' * bs
+                        for _ in range(size // bs):
+                            f.write(zeros)
+                        del zeros
+                    f.write(b'\0' * (size % bs))
+                    assert f.tell() == size
             self.buffer = mmap.mmap(self.fd, self.size)
 
     def reduce_arena(a):
diff --git a/Misc/ACKS b/Misc/ACKS
index 9a3de4e8333..d1074bda056 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -154,6 +154,7 @@ Wouter Bolsterlee
 Gawain Bolton
 Forest Bond
 Gregory Bond
+Médéric Boquien
 Matias Bordese
 Jonas Borgström
 Jurjen Bos
diff --git a/Misc/NEWS b/Misc/NEWS
index 78db876367b..e4574a11c35 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -29,6 +29,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #21116: Avoid blowing memory when allocating a multiprocessing shared
+  array that's larger than 50% of the available RAM.  Patch by Médéric Boquien.
+
 - Issue #22982: Improve BOM handling when seeking to multiple positions of
   a writable text file.