diff --git a/Lib/test/test_wsgiref.py b/Lib/test/test_wsgiref.py
index 05c1f4fc238..41076644295 100644
--- a/Lib/test/test_wsgiref.py
+++ b/Lib/test/test_wsgiref.py
@@ -286,7 +286,7 @@ class UtilityTests(TestCase):
     def testAppURIs(self):
         self.checkAppURI("http://127.0.0.1/")
         self.checkAppURI("http://127.0.0.1/spam", SCRIPT_NAME="/spam")
-        self.checkAppURI("http://127.0.0.1/sp%C3%A4m", SCRIPT_NAME="/späm")
+        self.checkAppURI("http://127.0.0.1/sp%E4m", SCRIPT_NAME="/sp\xe4m")
         self.checkAppURI("http://spam.example.com:2071/",
             HTTP_HOST="spam.example.com:2071", SERVER_PORT="2071")
         self.checkAppURI("http://spam.example.com/",
@@ -300,15 +300,19 @@ class UtilityTests(TestCase):
     def testReqURIs(self):
         self.checkReqURI("http://127.0.0.1/")
         self.checkReqURI("http://127.0.0.1/spam", SCRIPT_NAME="/spam")
-        self.checkReqURI("http://127.0.0.1/sp%C3%A4m", SCRIPT_NAME="/späm")
+        self.checkReqURI("http://127.0.0.1/sp%E4m", SCRIPT_NAME="/sp\xe4m")
         self.checkReqURI("http://127.0.0.1/spammity/spam",
             SCRIPT_NAME="/spammity", PATH_INFO="/spam")
+        self.checkReqURI("http://127.0.0.1/spammity/sp%E4m",
+            SCRIPT_NAME="/spammity", PATH_INFO="/sp\xe4m")
         self.checkReqURI("http://127.0.0.1/spammity/spam;ham",
             SCRIPT_NAME="/spammity", PATH_INFO="/spam;ham")
         self.checkReqURI("http://127.0.0.1/spammity/spam;cookie=1234,5678",
             SCRIPT_NAME="/spammity", PATH_INFO="/spam;cookie=1234,5678")
         self.checkReqURI("http://127.0.0.1/spammity/spam?say=ni",
             SCRIPT_NAME="/spammity", PATH_INFO="/spam",QUERY_STRING="say=ni")
+        self.checkReqURI("http://127.0.0.1/spammity/spam?s%E4y=ni",
+            SCRIPT_NAME="/spammity", PATH_INFO="/spam",QUERY_STRING="s%E4y=ni")
         self.checkReqURI("http://127.0.0.1/spammity/spam", 0,
             SCRIPT_NAME="/spammity", PATH_INFO="/spam",QUERY_STRING="say=ni")
 
diff --git a/Lib/wsgiref/util.py b/Lib/wsgiref/util.py
index 1f1e6cce179..516fe898d01 100644
--- a/Lib/wsgiref/util.py
+++ b/Lib/wsgiref/util.py
@@ -57,14 +57,14 @@ def application_uri(environ):
             if environ['SERVER_PORT'] != '80':
                 url += ':' + environ['SERVER_PORT']
 
-    url += quote(environ.get('SCRIPT_NAME') or '/')
+    url += quote(environ.get('SCRIPT_NAME') or '/', encoding='latin1')
     return url
 
 def request_uri(environ, include_query=True):
     """Return the full request URI, optionally including the query string"""
     url = application_uri(environ)
     from urllib.parse import quote
-    path_info = quote(environ.get('PATH_INFO',''),safe='/;=,')
+    path_info = quote(environ.get('PATH_INFO',''), safe='/;=,', encoding='latin1')
     if not environ.get('SCRIPT_NAME'):
         url += path_info[1:]
     else:
diff --git a/Misc/NEWS b/Misc/NEWS
index 552e949cdb5..6439b2ddd46 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -43,6 +43,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #20138: The wsgiref.application_uri() and wsgiref.request_uri()
+  functions now conform to PEP 3333 when handle non-ASCII URLs.
+
 - Issue #19097: Raise the correct Exception when cgi.FieldStorage is given an
   Invalid fileobj.