diff --git a/smart_open/http.py b/smart_open/http.py
index f3b3e40b..1510fce2 100644
--- a/smart_open/http.py
+++ b/smart_open/http.py
@@ -51,7 +51,7 @@ def open(uri, mode, kerberos=False, user=None, password=None, headers=None):
 
     """
     if mode == 'rb':
-        return BufferedInputBase(
+        return SeekableBufferedInputBase(
             uri, mode, kerberos=kerberos,
             user=user, password=password, headers=headers
         )
diff --git a/smart_open/tests/test_http.py b/smart_open/tests/test_http.py
index dacc71cd..c8fe86af 100644
--- a/smart_open/tests/test_http.py
+++ b/smart_open/tests/test_http.py
@@ -8,6 +8,7 @@
 
 BYTES = b'i tried so hard and got so far but in the end it doesn\'t even matter'
 URL = 'http://localhost'
+HTTPS_URL = 'https://localhost'
 HEADERS = {
     'Content-Length': str(len(BYTES)),
     'Accept-Ranges': 'bytes',
@@ -107,3 +108,35 @@ def test_headers(self):
         responses.add_callback(responses.GET, URL, callback=request_callback)
         reader = smart_open.http.open(URL, 'rb', headers={'Foo': 'bar'})
         self.assertEqual(reader.headers['Foo'], 'bar')
+
+    @responses.activate
+    def test_https_seek_start(self):
+        """Did the seek start over HTTPS work?"""
+        responses.add_callback(responses.GET, HTTPS_URL, callback=request_callback)
+
+        with smart_open.open(HTTPS_URL, "rb") as fin:
+            read_bytes_1 = fin.read(size=10)
+            fin.seek(0)
+            read_bytes_2 = fin.read(size=10)
+            self.assertEqual(read_bytes_1, read_bytes_2)
+
+    @responses.activate
+    def test_https_seek_forward(self):
+        """Did the seek forward over HTTPS work?"""
+        responses.add_callback(responses.GET, HTTPS_URL, callback=request_callback)
+
+        with smart_open.open(HTTPS_URL, "rb") as fin:
+            fin.seek(10)
+            read_bytes = fin.read(size=10)
+            self.assertEqual(BYTES[10:20], read_bytes)
+
+    @responses.activate
+    def test_https_seek_reverse(self):
+        """Did the seek in reverse over HTTPS work?"""
+        responses.add_callback(responses.GET, HTTPS_URL, callback=request_callback)
+
+        with smart_open.open(HTTPS_URL, "rb") as fin:
+            read_bytes_1 = fin.read(size=10)
+            fin.seek(-10, whence=smart_open.s3.CURRENT)
+            read_bytes_2 = fin.read(size=10)
+            self.assertEqual(read_bytes_1, read_bytes_2)