diff --git a/Lib/pickle.py b/Lib/pickle.py
index 3fc2596e675..663773f3d95 100644
--- a/Lib/pickle.py
+++ b/Lib/pickle.py
@@ -280,7 +280,9 @@ def whichmodule(obj, name, allow_qualname=False):
     module_name = getattr(obj, '__module__', None)
     if module_name is not None:
         return module_name
-    for module_name, module in sys.modules.items():
+    # Protect the iteration by using a list copy of sys.modules against dynamic
+    # modules that trigger imports of other modules upon calls to getattr.
+    for module_name, module in list(sys.modules.items()):
         if module_name == '__main__' or module is None:
             continue
         try:
diff --git a/Misc/ACKS b/Misc/ACKS
index 84dfd024ab1..ec8dc1ca813 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -498,6 +498,7 @@ Eddy De Greef
 Grant Griffin
 Andrea Griffini
 Duncan Grisby
+Olivier Grisel
 Fabian Groffen
 Eric Groo
 Dag Gruneau
diff --git a/Misc/NEWS b/Misc/NEWS
index 9e7efb9dfee..6b8ef3ec014 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -162,6 +162,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #21905: Avoid RuntimeError in pickle.whichmodule() when sys.modules
+  is mutated while iterating.  Patch by Olivier Grisel.
+
 - Issue #11271: concurrent.futures.Executor.map() now takes a *chunksize*
   argument to allow batching of tasks in child processes and improve
   performance of ProcessPoolExecutor.  Patch by Dan O'Reilly.