diff --git a/src/sage/misc/cython.py b/src/sage/misc/cython.py
index 93ce994c537..7590158b279 100644
--- a/src/sage/misc/cython.py
+++ b/src/sage/misc/cython.py
@@ -236,7 +236,7 @@ def cython(filename, verbose=0, compile_message=False,
         ...
         RuntimeError: Error compiling Cython file:
         ...
-        ...: 'sage/misc.pxd' not found
+        ...: 'sage/misc.pxd' not found...
     """
     if not filename.endswith('pyx'):
         print("Warning: file (={}) should have extension .pyx".format(filename), file=sys.stderr)
@@ -382,6 +382,12 @@ def cython(filename, verbose=0, compile_message=False,
             "Placing it before 'except' or 'noexcept' will be disallowed in a future version of Cython.\n",
             "", cython_messages, 0, re.MULTILINE)
 
+        # workaround for https://github.com/sagemath/sage/issues/37560
+        # triggered by Cython 3.0.9
+        cython_messages = re.sub(
+            "^warning: .*noexcept clause is ignored for function returning Python object\n",
+            "", cython_messages, 0, re.MULTILINE)
+
         sys.stderr.write(cython_messages)
         sys.stderr.flush()