diff --git a/Lib/ctypes/test/test_callbacks.py b/Lib/ctypes/test/test_callbacks.py
index f622093df61..937a06d981b 100644
--- a/Lib/ctypes/test/test_callbacks.py
+++ b/Lib/ctypes/test/test_callbacks.py
@@ -287,6 +287,21 @@ class SampleCallbacksTestCase(unittest.TestCase):
         self.assertEqual(s.second, check.second)
         self.assertEqual(s.third, check.third)
 
+    def test_callback_too_many_args(self):
+        def func(*args):
+            return len(args)
+
+        CTYPES_MAX_ARGCOUNT = 1024
+        proto = CFUNCTYPE(c_int, *(c_int,) * CTYPES_MAX_ARGCOUNT)
+        cb = proto(func)
+        args1 = (1,) * CTYPES_MAX_ARGCOUNT
+        self.assertEqual(cb(*args1), CTYPES_MAX_ARGCOUNT)
+
+        args2 = (1,) * (CTYPES_MAX_ARGCOUNT + 1)
+        with self.assertRaises(ArgumentError):
+            cb(*args2)
+
+
 ################################################################
 
 if __name__ == '__main__':
diff --git a/Misc/NEWS.d/next/Library/2020-05-06-02-01-25.bpo-13097.Wh5xSK.rst b/Misc/NEWS.d/next/Library/2020-05-06-02-01-25.bpo-13097.Wh5xSK.rst
new file mode 100644
index 00000000000..a7f5f588289
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-05-06-02-01-25.bpo-13097.Wh5xSK.rst
@@ -0,0 +1 @@
+``ctypes`` now raises an ``ArgumentError`` when a callback is invoked with more than 1024 arguments.
\ No newline at end of file
diff --git a/Modules/_ctypes/callproc.c b/Modules/_ctypes/callproc.c
index 4027bdb6227..e0a110d3f46 100644
--- a/Modules/_ctypes/callproc.c
+++ b/Modules/_ctypes/callproc.c
@@ -1073,6 +1073,14 @@ GetComError(HRESULT errcode, GUID *riid, IUnknown *pIunk)
 #define IS_PASS_BY_REF(x) (x > 8 || !POW2(x))
 #endif
 
+/*
+ * bpo-13097: Max number of arguments _ctypes_callproc will accept.
+ *
+ * This limit is enforced for the `alloca()` call in `_ctypes_callproc`,
+ * to avoid allocating a massive buffer on the stack.
+ */
+#define CTYPES_MAX_ARGCOUNT 1024
+
 /*
  * Requirements, must be ensured by the caller:
  * - argtuple is tuple of arguments
@@ -1108,6 +1116,13 @@ PyObject *_ctypes_callproc(PPROC pProc,
         ++argcount;
 #endif
 
+    if (argcount > CTYPES_MAX_ARGCOUNT)
+    {
+        PyErr_Format(PyExc_ArgError, "too many arguments (%zi), maximum is %i",
+                     argcount, CTYPES_MAX_ARGCOUNT);
+        return NULL;
+    }
+
     args = (struct argument *)alloca(sizeof(struct argument) * argcount);
     if (!args) {
         PyErr_NoMemory();