diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 5d496c6687614b..27cb884e072e05 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -3831,6 +3831,7 @@ def test_min_max_version_tlsv1_1(self):
 
     @requires_minimum_version
     @requires_tls_version('TLSv1_2')
+    @requires_tls_version('TLSv1')
     def test_min_max_version_mismatch(self):
         client_context, server_context, hostname = testing_context()
         # client 1.0, server 1.2 (mismatch)
diff --git a/Misc/NEWS.d/next/Tests/2020-09-18-16-14-03.bpo-41561.uPnwrW.rst b/Misc/NEWS.d/next/Tests/2020-09-18-16-14-03.bpo-41561.uPnwrW.rst
new file mode 100644
index 00000000000000..10bce825961c3c
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2020-09-18-16-14-03.bpo-41561.uPnwrW.rst
@@ -0,0 +1 @@
+test_ssl: skip test_min_max_version_mismatch when TLS 1.0 is not available