diff --git a/tornado/test/testing_test.py b/tornado/test/testing_test.py
index 0429feee83..8e2b8db428 100644
--- a/tornado/test/testing_test.py
+++ b/tornado/test/testing_test.py
@@ -61,6 +61,15 @@ def test_subsequent_wait_calls(self):
         self.io_loop.add_timeout(self.io_loop.time() + 0.2, self.stop)
         self.wait(timeout=0.4)
 
+    def test_empty_instantation_is_allowed(self):
+        """
+        Test that empty instatiation of an AsyncTestCase is allowed.
+
+        unittest.TestCase docs guarantee this working, and pytest's unittest
+        support relies on it.
+        """
+        AsyncTestCaseTest()
+
 
 class LeakTest(AsyncTestCase):
     def tearDown(self):
diff --git a/tornado/testing.py b/tornado/testing.py
index bdbff87bc3..9455411a6d 100644
--- a/tornado/testing.py
+++ b/tornado/testing.py
@@ -177,7 +177,17 @@ def __init__(self, methodName: str = "runTest") -> None:
         # the test will silently be ignored because nothing will consume
         # the generator.  Replace the test method with a wrapper that will
         # make sure it's not an undecorated generator.
-        setattr(self, methodName, _TestMethodWrapper(getattr(self, methodName)))
+        try:
+            test_method = getattr(self, methodName)
+        except AttributeError:
+            if methodName != "runTest":
+                # We allow instantiation with no explicit method name
+                # but not an *incorrect* or missing method name.
+                raise ValueError(
+                    "no such test method in %s: %s" % (self.__class__, methodName)
+                )
+        else:
+            setattr(self, methodName, _TestMethodWrapper(test_method))
 
         # Not used in this class itself, but used by @gen_test
         self._test_generator = None  # type: Optional[Union[Generator, Coroutine]]