diff --git a/Lib/base64.py b/Lib/base64.py
--- a/Lib/base64.py
+++ b/Lib/base64.py
@@ -27,7 +27,7 @@
     ]
 
 
-bytes_types = (bytes, bytearray)  # Types acceptable as binary data
+bytes_types = (bytes, bytearray, memoryview)  # Types acceptable as binary data
 
 def _bytes_from_decode_data(s):
     if isinstance(s, str):
@@ -161,6 +161,8 @@
     """
     if not isinstance(s, bytes_types):
         raise TypeError("expected bytes, not %s" % s.__class__.__name__)
+    if isinstance(s, memoryview):
+        s = s.tobytes()
     quanta, leftover = divmod(len(s), 5)
     # Pad the last quantum with zero bits if necessary
     if leftover:
diff --git a/Lib/test/test_base64.py b/Lib/test/test_base64.py
--- a/Lib/test/test_base64.py
+++ b/Lib/test/test_base64.py
@@ -15,6 +15,8 @@
         eq(base64.encodebytes(b"a"), b"YQ==\n")
         eq(base64.encodebytes(b"ab"), b"YWI=\n")
         eq(base64.encodebytes(b"abc"), b"YWJj\n")
+        # Test for memoryview, issue17839
+        eq(base64.encodebytes(memoryview(b"abc")), b"YWJj\n")
         eq(base64.encodebytes(b""), b"")
         eq(base64.encodebytes(b"abcdefghijklmnopqrstuvwxyz"
                                b"ABCDEFGHIJKLMNOPQRSTUVWXYZ"
@@ -69,6 +71,8 @@
         eq(base64.b64encode(b"a"), b"YQ==")
         eq(base64.b64encode(b"ab"), b"YWI=")
         eq(base64.b64encode(b"abc"), b"YWJj")
+        # Test for memoryview, issue17839
+        eq(base64.b64encode(memoryview(b"abc")), b"YWJj")
         eq(base64.b64encode(b""), b"")
         eq(base64.b64encode(b"abcdefghijklmnopqrstuvwxyz"
                             b"ABCDEFGHIJKLMNOPQRSTUVWXYZ"
@@ -86,6 +90,8 @@
         eq(base64.standard_b64encode(b"a"), b"YQ==")
         eq(base64.standard_b64encode(b"ab"), b"YWI=")
         eq(base64.standard_b64encode(b"abc"), b"YWJj")
+        # Test for memoryview, issue17839
+        eq(base64.standard_b64encode(memoryview(b"abc")), b"YWJj")
         eq(base64.standard_b64encode(b""), b"")
         eq(base64.standard_b64encode(b"abcdefghijklmnopqrstuvwxyz"
                                      b"ABCDEFGHIJKLMNOPQRSTUVWXYZ"
@@ -180,6 +186,8 @@
         eq(base64.b32encode(b'abcd'), b'MFRGGZA=')
         eq(base64.b32encode(b'abcde'), b'MFRGGZDF')
         self.assertRaises(TypeError, base64.b32encode, "")
+        # Test for memoryview, issue17839
+        eq(base64.b32encode(memoryview(b'abcde')), b'MFRGGZDF')
 
     def test_b32decode(self):
         eq = self.assertEqual
@@ -246,6 +254,8 @@
         eq(base64.b16encode(b'\x01\x02\xab\xcd\xef'), b'0102ABCDEF')
         eq(base64.b16encode(b'\x00'), b'00')
         self.assertRaises(TypeError, base64.b16encode, "")
+        # Test for memoryview, issue17839
+        eq(base64.b16encode(memoryview(b'\x01\x02\xab\xcd\xef')), b'0102ABCDEF')
 
     def test_b16decode(self):
         eq = self.assertEqual