diff --git a/tornado/httputil.py b/tornado/httputil.py
index b21d8046c4..9ce992d82b 100644
--- a/tornado/httputil.py
+++ b/tornado/httputil.py
@@ -62,6 +62,9 @@
     from asyncio import Future  # noqa: F401
     import unittest  # noqa: F401
 
+# To be used with str.strip() and related methods.
+HTTP_WHITESPACE = " \t"
+
 
 @lru_cache(1000)
 def _normalize_header(name: str) -> str:
@@ -171,7 +174,7 @@ def parse_line(self, line: str) -> None:
             # continuation of a multi-line header
             if self._last_key is None:
                 raise HTTPInputError("first header line cannot start with whitespace")
-            new_part = " " + line.lstrip()
+            new_part = " " + line.lstrip(HTTP_WHITESPACE)
             self._as_list[self._last_key][-1] += new_part
             self._dict[self._last_key] += new_part
         else:
@@ -179,7 +182,7 @@ def parse_line(self, line: str) -> None:
                 name, value = line.split(":", 1)
             except ValueError:
                 raise HTTPInputError("no colon in header line")
-            self.add(name, value.strip())
+            self.add(name, value.strip(HTTP_WHITESPACE))
 
     @classmethod
     def parse(cls, headers: str) -> "HTTPHeaders":
diff --git a/tornado/test/httputil_test.py b/tornado/test/httputil_test.py
index aa9b6ee253..6d618839e0 100644
--- a/tornado/test/httputil_test.py
+++ b/tornado/test/httputil_test.py
@@ -334,6 +334,25 @@ def test_unicode_newlines(self):
                     gen_log.warning("failed while trying %r in %s", newline, encoding)
                     raise
 
+    def test_unicode_whitespace(self):
+        # Only tabs and spaces are to be stripped according to the HTTP standard.
+        # Other unicode whitespace is to be left as-is. In the context of headers,
+        # this specifically means the whitespace characters falling within the
+        # latin1 charset.
+        whitespace = [
+            (" ", True),  # SPACE
+            ("\t", True),  # TAB
+            ("\u00a0", False),  # NON-BREAKING SPACE
+            ("\u0085", False),  # NEXT LINE
+        ]
+        for c, stripped in whitespace:
+            headers = HTTPHeaders.parse("Transfer-Encoding: %schunked" % c)
+            if stripped:
+                expected = [("Transfer-Encoding", "chunked")]
+            else:
+                expected = [("Transfer-Encoding", "%schunked" % c)]
+            self.assertEqual(expected, list(headers.get_all()))
+
     def test_optional_cr(self):
         # Both CRLF and LF should be accepted as separators. CR should not be
         # part of the data when followed by LF, but it is a normal char