diff --git a/mypy/semanal_classprop.py b/mypy/semanal_classprop.py
index 8f8ccd91fc6b5..c9772276d7d8a 100644
--- a/mypy/semanal_classprop.py
+++ b/mypy/semanal_classprop.py
@@ -30,6 +30,7 @@
 TYPE_PROMOTIONS_PYTHON3 = TYPE_PROMOTIONS.copy()  # type: Final
 TYPE_PROMOTIONS_PYTHON3.update({
     'builtins.bytearray': 'bytes',
+    'builtins.memoryview': 'bytes',
 })
 
 # Hard coded type promotions for Python 2.
@@ -41,6 +42,7 @@
 TYPE_PROMOTIONS_PYTHON2.update({
     'builtins.str': 'unicode',
     'builtins.bytearray': 'str',
+    'builtins.memoryview': 'str',
 })
 
 
diff --git a/test-data/unit/check-type-promotion.test b/test-data/unit/check-type-promotion.test
index b0ee0a2ec9d8a..f477a9f2b390e 100644
--- a/test-data/unit/check-type-promotion.test
+++ b/test-data/unit/check-type-promotion.test
@@ -26,6 +26,11 @@ def f(x: bytes) -> None: pass
 f(bytearray(b''))
 [builtins fixtures/primitives.pyi]
 
+[case testPromoteMemoryviewToBytes]
+def f(x: bytes) -> None: pass
+f(memoryview(b''))
+[builtins fixtures/primitives.pyi]
+
 [case testNarrowingDownFromPromoteTargetType]
 y = 0.0
 y = 1
diff --git a/test-data/unit/fixtures/primitives.pyi b/test-data/unit/fixtures/primitives.pyi
index 6043c6210d5ac..5e3b7ab32f7a5 100644
--- a/test-data/unit/fixtures/primitives.pyi
+++ b/test-data/unit/fixtures/primitives.pyi
@@ -35,6 +35,11 @@ class bytearray(Sequence[int]):
     def __iter__(self) -> Iterator[int]: pass
     def __contains__(self, other: object) -> bool: pass
     def __getitem__(self, item: int) -> int: pass
+class memoryview(Sequence[int]):
+    def __init__(self, x: bytes) -> None: pass
+    def __iter__(self) -> Iterator[int]: pass
+    def __contains__(self, other: object) -> bool: pass
+    def __getitem__(self, item: int) -> int: pass
 class tuple(Generic[T]): pass
 class list(Sequence[T]):
     def __iter__(self) -> Iterator[T]: pass