diff --git a/src/flask/app.py b/src/flask/app.py
index f4d35658..eaeb613e 100644
--- a/src/flask/app.py
+++ b/src/flask/app.py
@@ -1,5 +1,6 @@
 import os
 import sys
+import weakref
 from datetime import timedelta
 from itertools import chain
 from threading import Lock
@@ -478,11 +479,14 @@ class Flask(Scaffold):
             assert (
                 bool(static_host) == host_matching
             ), "Invalid static_host/host_matching combination"
+            # Use a weakref to avoid creating a reference cycle between the app
+            # and the view function (see #3761).
+            self_ref = weakref.ref(self)
             self.add_url_rule(
                 f"{self.static_url_path}/<path:filename>",
                 endpoint="static",
                 host=static_host,
-                view_func=self.send_static_file,
+                view_func=lambda **kw: self_ref().send_static_file(**kw),
             )
 
         # Set the name of the Click group in case someone wants to add
diff --git a/tests/test_basic.py b/tests/test_basic.py
index 6c45b008..76d3e1fc 100644
--- a/tests/test_basic.py
+++ b/tests/test_basic.py
@@ -1,8 +1,11 @@
+import gc
 import re
 import sys
 import time
 import uuid
+import weakref
 from datetime import datetime
+from platform import python_implementation
 from threading import Thread
 
 import pytest
@@ -16,6 +19,11 @@ from werkzeug.routing import BuildError
 import flask
 
 
+require_cpython_gc = pytest.mark.skipif(
+    python_implementation() != "CPython", reason="Requires CPython GC behavior",
+)
+
+
 def test_options_work(app, client):
     @app.route("/", methods=["GET", "POST"])
     def index():
@@ -1970,3 +1978,19 @@ def test_max_cookie_size(app, client, recwarn):
 
     client.get("/")
     assert len(recwarn) == 0
+
+
+@require_cpython_gc
+def test_app_freed_on_zero_refcount():
+    # A Flask instance should not create a reference cycle that prevents CPython
+    # from freeing it when all external references to it are released (see #3761).
+    gc.disable()
+    try:
+        app = flask.Flask(__name__)
+        assert app.view_functions["static"]
+        weak = weakref.ref(app)
+        assert weak() is not None
+        del app
+        assert weak() is None
+    finally:
+        gc.enable()