diff --git a/frontend_tests/node_tests/markdown.js b/frontend_tests/node_tests/markdown.js
index 7ae95b84a2..ff75407356 100644
--- a/frontend_tests/node_tests/markdown.js
+++ b/frontend_tests/node_tests/markdown.js
@@ -425,6 +425,18 @@ run_test('topic_links', () => {
     assert.equal(util.get_topic_links(message).length, 1);
     assert.equal(util.get_topic_links(message)[0], "https://zone_45.zulip.net/ticket/123");
 
+    message = {type: 'stream', topic: "Hello https://google.com"};
+    markdown.add_topic_links(message);
+    assert.equal(util.get_topic_links(message).length, 1);
+    assert.equal(util.get_topic_links(message)[0], "https://google.com");
+
+    message = {type: 'stream', topic: "#456 https://google.com https://github.com"};
+    markdown.add_topic_links(message);
+    assert.equal(util.get_topic_links(message).length, 3);
+    assert(util.get_topic_links(message).indexOf("https://google.com") !== -1);
+    assert(util.get_topic_links(message).indexOf("https://github.com") !== -1);
+    assert(util.get_topic_links(message).indexOf("https://trac.zulip.net/ticket/456") !== -1);
+
     message = {type: "not-stream"};
     markdown.add_topic_links(message);
     assert.equal(util.get_topic_links(message).length, 0);
diff --git a/static/js/markdown.js b/static/js/markdown.js
index 26695b1886..20b79314dc 100644
--- a/static/js/markdown.js
+++ b/static/js/markdown.js
@@ -160,6 +160,14 @@ exports.add_topic_links = function (message) {
             links.push(link_url);
         }
     });
+
+    // Also make raw urls navigable
+    var url_re = /\b(https?:\/\/[^\s<]+[^<.,:;"')\]\s])/g; // Slightly modified from third/marked.js
+    var match = topic.match(url_re);
+    if (match) {
+        links = links.concat(match);
+    }
+
     util.set_topic_links(message, links);
 };
 
diff --git a/zerver/lib/bugdown/__init__.py b/zerver/lib/bugdown/__init__.py
index 6f5b67c212..3d124d7c76 100644
--- a/zerver/lib/bugdown/__init__.py
+++ b/zerver/lib/bugdown/__init__.py
@@ -1969,6 +1969,10 @@ def build_engine(realm_filters: List[Tuple[str, str, int]],
         ])
     return engine
 
+# Split the topic name into multiple sections so that we can easily use
+# our common single link matching regex on it.
+basic_link_splitter = re.compile(r'[ !;\?\),\'\"]')
+
 # Security note: We don't do any HTML escaping in this
 # function on the URLs; they are expected to be HTML-escaped when
 # rendered by clients (just as links rendered into message bodies
@@ -1982,6 +1986,13 @@ def topic_links(realm_filters_key: int, topic_name: str) -> List[str]:
         pattern = prepare_realm_pattern(realm_filter[0])
         for m in re.finditer(pattern, topic_name):
             matches += [realm_filter[1] % m.groupdict()]
+
+    # Also make raw urls navigable.
+    for sub_string in basic_link_splitter.split(topic_name):
+        link_match = re.match(get_web_link_regex(), sub_string)
+        if link_match:
+            matches.append(link_match.group('url'))
+
     return matches
 
 def maybe_update_markdown_engines(realm_filters_key: Optional[int], email_gateway: bool) -> None:
diff --git a/zerver/tests/test_bugdown.py b/zerver/tests/test_bugdown.py
index 54da194b48..6faac7b3a6 100644
--- a/zerver/tests/test_bugdown.py
+++ b/zerver/tests/test_bugdown.py
@@ -787,6 +787,18 @@ class BugdownTest(ZulipTestCase):
         converted = bugdown_convert(msg)
         self.assertEqual(converted, unicode_converted)
 
+    def test_links_in_topic_name(self) -> None:
+        realm = get_realm('zulip')
+        msg = Message(sender=self.example_user('othello'))
+
+        msg.set_topic_name("https://google.com/hello-world")
+        converted_topic = bugdown.topic_links(realm.id, msg.topic_name())
+        self.assertEqual(converted_topic, [u'https://google.com/hello-world'])
+
+        msg.set_topic_name("Try out http://ftp.debian.org, https://google.com/ and https://google.in/.")
+        converted_topic = bugdown.topic_links(realm.id, msg.topic_name())
+        self.assertEqual(converted_topic, [u'http://ftp.debian.org', 'https://google.com/', 'https://google.in/'])
+
     def test_realm_patterns(self) -> None:
         realm = get_realm('zulip')
         url_format_string = r"https://trac.zulip.net/ticket/%(id)s"
@@ -811,6 +823,10 @@ class BugdownTest(ZulipTestCase):
         self.assertEqual(converted, '<p>We should fix <a href="https://trac.zulip.net/ticket/224" target="_blank" title="https://trac.zulip.net/ticket/224">#224</a> and <a href="https://trac.zulip.net/ticket/115" target="_blank" title="https://trac.zulip.net/ticket/115">#115</a>, but not issue#124 or #1124z or <a href="https://trac.zulip.net/ticket/16" target="_blank" title="https://trac.zulip.net/ticket/16">trac #15</a> today.</p>')
         self.assertEqual(converted_topic, [u'https://trac.zulip.net/ticket/444'])
 
+        msg.set_topic_name("#444 https://google.com")
+        converted_topic = bugdown.topic_links(realm.id, msg.topic_name())
+        self.assertEqual(converted_topic, [u'https://trac.zulip.net/ticket/444', u'https://google.com'])
+
         RealmFilter(realm=realm, pattern=r'#(?P<id>[a-zA-Z]+-[0-9]+)',
                     url_format_string=r'https://trac.zulip.net/ticket/%(id)s').save()
         msg = Message(sender=self.example_user('hamlet'))