diff --git a/CHANGES.rst b/CHANGES.rst
index 7920e5ab..be263970 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -10,6 +10,7 @@ Unreleased
     decorators. :issue:`4104`
 -   Fixed the issue where typing requires template global
     decorators to accept functions with no arguments. :issue:`4098`
+-   Support View and MethodView instances with async handlers. :issue:`4112`
 
 
 Version 2.0.1
diff --git a/docs/async-await.rst b/docs/async-await.rst
index ad7cbf38..71e5f452 100644
--- a/docs/async-await.rst
+++ b/docs/async-await.rst
@@ -18,6 +18,12 @@ defined with ``async def`` and use ``await``.
         data = await async_db_query(...)
         return jsonify(data)
 
+Pluggable class-based views also support handlers that are implemented as
+coroutines. This applies to the :meth:`~flask.views.View.dispatch_request`
+method in views that inherit from the :class:`flask.views.View` class, as
+well as all the HTTP method handlers in views that inherit from the
+:class:`flask.views.MethodView` class.
+
 .. admonition:: Using ``async`` on Windows on Python 3.8
 
     Python 3.8 has a bug related to asyncio on Windows. If you encounter
diff --git a/src/flask/views.py b/src/flask/views.py
index 339ffa18..1bd5c68b 100644
--- a/src/flask/views.py
+++ b/src/flask/views.py
@@ -1,5 +1,6 @@
 import typing as t
 
+from .globals import current_app
 from .globals import request
 from .typing import ResponseReturnValue
 
@@ -80,7 +81,7 @@ class View:
 
         def view(*args: t.Any, **kwargs: t.Any) -> ResponseReturnValue:
             self = view.view_class(*class_args, **class_kwargs)  # type: ignore
-            return self.dispatch_request(*args, **kwargs)
+            return current_app.ensure_sync(self.dispatch_request)(*args, **kwargs)
 
         if cls.decorators:
             view.__name__ = name
@@ -154,4 +155,4 @@ class MethodView(View, metaclass=MethodViewType):
             meth = getattr(self, "get", None)
 
         assert meth is not None, f"Unimplemented method {request.method!r}"
-        return meth(*args, **kwargs)
+        return current_app.ensure_sync(meth)(*args, **kwargs)
diff --git a/tests/test_async.py b/tests/test_async.py
index 26a91118..344e9fe6 100644
--- a/tests/test_async.py
+++ b/tests/test_async.py
@@ -6,6 +6,8 @@ import pytest
 from flask import Blueprint
 from flask import Flask
 from flask import request
+from flask.views import MethodView
+from flask.views import View
 
 pytest.importorskip("asgiref")
 
@@ -18,6 +20,24 @@ class BlueprintError(Exception):
     pass
 
 
+class AsyncView(View):
+    methods = ["GET", "POST"]
+
+    async def dispatch_request(self):
+        await asyncio.sleep(0)
+        return request.method
+
+
+class AsyncMethodView(MethodView):
+    async def get(self):
+        await asyncio.sleep(0)
+        return 'GET'
+
+    async def post(self):
+        await asyncio.sleep(0)
+        return 'POST'
+
+
 @pytest.fixture(name="async_app")
 def _async_app():
     app = Flask(__name__)
@@ -53,11 +73,14 @@ def _async_app():
 
     app.register_blueprint(blueprint, url_prefix="/bp")
 
+    app.add_url_rule('/view', view_func=AsyncView.as_view('view'))
+    app.add_url_rule('/methodview', view_func=AsyncMethodView.as_view('methodview'))
+
     return app
 
 
 @pytest.mark.skipif(sys.version_info < (3, 7), reason="requires Python >= 3.7")
-@pytest.mark.parametrize("path", ["/", "/home", "/bp/"])
+@pytest.mark.parametrize("path", ["/", "/home", "/bp/", "/view", "/methodview"])
 def test_async_route(path, async_app):
     test_client = async_app.test_client()
     response = test_client.get(path)