diff --git a/Lib/test/test_textwrap.py b/Lib/test/test_textwrap.py
index a44184fbc77..5a33c151642 100644
--- a/Lib/test/test_textwrap.py
+++ b/Lib/test/test_textwrap.py
@@ -444,6 +444,37 @@ What a mess!
         text = "aa \xe4\xe4-\xe4\xe4"
         self.check_wrap(text, 7, ["aa \xe4\xe4-", "\xe4\xe4"])
 
+    def test_non_breaking_space(self):
+        text = 'This is a sentence with non-breaking\N{NO-BREAK SPACE}space.'
+
+        self.check_wrap(text, 20,
+                        ['This is a sentence',
+                         'with non-',
+                         'breaking\N{NO-BREAK SPACE}space.'],
+                        break_on_hyphens=True)
+
+        self.check_wrap(text, 20,
+                        ['This is a sentence',
+                         'with',
+                         'non-breaking\N{NO-BREAK SPACE}space.'],
+                        break_on_hyphens=False)
+
+    def test_narrow_non_breaking_space(self):
+        text = ('This is a sentence with non-breaking'
+                '\N{NARROW NO-BREAK SPACE}space.')
+
+        self.check_wrap(text, 20,
+                        ['This is a sentence',
+                         'with non-',
+                         'breaking\N{NARROW NO-BREAK SPACE}space.'],
+                        break_on_hyphens=True)
+
+        self.check_wrap(text, 20,
+                        ['This is a sentence',
+                         'with',
+                         'non-breaking\N{NARROW NO-BREAK SPACE}space.'],
+                        break_on_hyphens=False)
+
 
 class MaxLinesTestCase(BaseTestCase):
     text = "Hello there, how are you this fine day?  I'm glad to hear it!"
diff --git a/Lib/textwrap.py b/Lib/textwrap.py
index 05e030673a6..0c18dc582e1 100644
--- a/Lib/textwrap.py
+++ b/Lib/textwrap.py
@@ -10,13 +10,8 @@ import re
 __all__ = ['TextWrapper', 'wrap', 'fill', 'dedent', 'indent', 'shorten']
 
 # Hardcode the recognized whitespace characters to the US-ASCII
-# whitespace characters.  The main reason for doing this is that in
-# ISO-8859-1, 0xa0 is non-breaking whitespace, so in certain locales
-# that character winds up in string.whitespace.  Respecting
-# string.whitespace in those cases would 1) make textwrap treat 0xa0 the
-# same as any other whitespace char, which is clearly wrong (it's a
-# *non-breaking* space), 2) possibly cause problems with Unicode,
-# since 0xa0 is not in range(128).
+# whitespace characters.  The main reason for doing this is that
+# some Unicode spaces (like \u00a0) are non-breaking whitespaces.
 _whitespace = '\t\n\x0b\x0c\r '
 
 class TextWrapper:
@@ -81,29 +76,34 @@ class TextWrapper:
     # (after stripping out empty strings).
     word_punct = r'[\w!"\'&.,?]'
     letter = r'[^\d\W]'
+    whitespace = r'[%s]' % re.escape(_whitespace)
+    nowhitespace = '[^' + whitespace[1:]
     wordsep_re = re.compile(r'''
         ( # any whitespace
-          \s+
+          %(ws)s+
         | # em-dash between words
           (?<=%(wp)s) -{2,} (?=\w)
         | # word, possibly hyphenated
-          \S+? (?:
+          %(nws)s+? (?:
             # hyphenated word
               -(?: (?<=%(lt)s{2}-) | (?<=%(lt)s-%(lt)s-))
               (?= %(lt)s -? %(lt)s)
             | # end of word
-              (?=\s|\Z)
+              (?=%(ws)s|\Z)
             | # em-dash
               (?<=%(wp)s) (?=-{2,}\w)
             )
-        )''' % {'wp': word_punct, 'lt': letter}, re.VERBOSE)
-    del word_punct, letter
+        )''' % {'wp': word_punct, 'lt': letter,
+                'ws': whitespace, 'nws': nowhitespace},
+        re.VERBOSE)
+    del word_punct, letter, nowhitespace
 
     # This less funky little regex just split on recognized spaces. E.g.
     #   "Hello there -- you goof-ball, use the -b option!"
     # splits into
     #   Hello/ /there/ /--/ /you/ /goof-ball,/ /use/ /the/ /-b/ /option!/
-    wordsep_simple_re = re.compile(r'(\s+)')
+    wordsep_simple_re = re.compile(r'(%s+)' % whitespace)
+    del whitespace
 
     # XXX this is not locale- or charset-aware -- string.lowercase
     # is US-ASCII only (and therefore English-only)
@@ -112,7 +112,6 @@ class TextWrapper:
                                  r'[\"\']?'           # optional end-of-quote
                                  r'\Z')               # end of chunk
 
-
     def __init__(self,
                  width=70,
                  initial_indent="",
diff --git a/Misc/NEWS b/Misc/NEWS
index ea90cbb9da6..c4405716347 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -113,6 +113,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #20491: The textwrap.TextWrapper class now honors non-breaking spaces.
+  Based on patch by Kaarle Ritvanen.
+
 - Issue #28353: os.fwalk() no longer fails on broken links.
 
 - Issue #25464: Fixed HList.header_exists() in tkinter.tix module by addin