diff --git a/Lib/doctest.py b/Lib/doctest.py
index ee71984a7d97cf..3f6a65c037370a 100644
--- a/Lib/doctest.py
+++ b/Lib/doctest.py
@@ -994,9 +994,15 @@ def _find(self, tests, obj, name, module, source_lines, globs, seen):
         if inspect.ismodule(obj) and self._recurse:
             for valname, val in obj.__dict__.items():
                 valname = '%s.%s' % (name, valname)
+
+                # Protect against objects that cause unwrap to throw
+                isroutine = False
+                try:
+                    isroutine = inspect.isroutine(inspect.unwrap(val))
+                except ValueError:
+                    pass
                 # Recurse to functions & classes.
-                if ((inspect.isroutine(inspect.unwrap(val))
-                     or inspect.isclass(val)) and
+                if ((isroutine or inspect.isclass(val)) and
                     self._from_module(module, val)):
                     self._find(tests, val, valname, module, source_lines,
                                globs, seen)
diff --git a/Lib/test/test_doctest5.py b/Lib/test/test_doctest5.py
new file mode 100644
index 00000000000000..74a4ac0b6dcd86
--- /dev/null
+++ b/Lib/test/test_doctest5.py
@@ -0,0 +1,33 @@
+"""A module to test whether doctest works properly with
+un-unwrappable functions.
+
+See: https://bugs.python.org/issue35753
+"""
+
+# This should trigger issue35753 when doctest called
+from unittest.mock import call
+
+import sys
+import unittest
+from test import support
+if sys.flags.optimize >= 2:
+    raise unittest.SkipTest("Cannot test docstrings with -O2")
+
+
+def test_main():
+    from test import test_doctest5
+    EXPECTED = 0
+    try:
+        f, t = support.run_doctest(test_doctest5)
+        if t != EXPECTED:
+            raise support.TestFailed("expected %d tests to run, not %d" %
+                                          (EXPECTED, t))
+    except ValueError as e:
+        raise support.TestFailed("Doctest unwrap failed") from e
+
+# Pollute the namespace with a bunch of imported functions and classes,
+# to make sure they don't get tested.
+# from doctest import *
+
+if __name__ == '__main__':
+    test_main()
diff --git a/Misc/NEWS.d/next/Tests/2020-10-25-19-20-26.bpo-35753.2LT-hO.rst b/Misc/NEWS.d/next/Tests/2020-10-25-19-20-26.bpo-35753.2LT-hO.rst
new file mode 100644
index 00000000000000..eddfc25906da9e
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2020-10-25-19-20-26.bpo-35753.2LT-hO.rst
@@ -0,0 +1,2 @@
+Fix crash in doctest when doctest parses modules that include unwrappable
+functions by skipping those functions.