diff --git a/sanic/app.py b/sanic/app.py
index 22435ef610..6b547eea9c 100644
--- a/sanic/app.py
+++ b/sanic/app.py
@@ -1209,10 +1209,15 @@ async def handle_exception(
         # Request Middleware
         # -------------------------------------------- #
         if run_middleware:
-            middleware = (
-                request.route and request.route.extra.request_middleware
-            ) or self.request_middleware
-            response = await self._run_request_middleware(request, middleware)
+            try:
+                middleware = (
+                    request.route and request.route.extra.request_middleware
+                ) or self.request_middleware
+                response = await self._run_request_middleware(
+                    request, middleware
+                )
+            except Exception as e:
+                return await self.handle_exception(request, e, False)
         # No middleware results
         if not response:
             try:
diff --git a/tests/test_exceptions.py b/tests/test_exceptions.py
index 7932eb6dfb..b945eadea0 100644
--- a/tests/test_exceptions.py
+++ b/tests/test_exceptions.py
@@ -1,5 +1,7 @@
 import logging
 
+from itertools import count
+
 import pytest
 
 from bs4 import BeautifulSoup
@@ -413,3 +415,21 @@ class CustomError(SanicException):
     assert CustomError().message == CustomError.message == str(CustomError())
     assert SanicException().message != ""
     assert SanicException("").message == ""
+
+
+def test_request_middleware_exception_on_404(app: Sanic):
+    """See https://github.com/sanic-org/sanic/issues/2950"""
+    counter = count()
+
+    @app.on_request
+    def request_middleware(request):
+        value = next(counter)
+        raise Exception
+
+    @app.route("/")
+    async def handler(request): ...
+
+    _, response = app.test_client.get("/not-found")
+
+    assert response.status == 500
+    assert next(counter) == 1