diff --git a/mesonbuild/modules/python.py b/mesonbuild/modules/python.py
index b100d86d8d39..45d024d28fe4 100644
--- a/mesonbuild/modules/python.py
+++ b/mesonbuild/modules/python.py
@@ -216,8 +216,24 @@ def extension_module_method(self, args: T.Tuple[str, T.List[BuildTargetSource]],
                 kwargs['link_args'] = new_link_args
 
             cython_compiler = next((c for c in compilers.values() if c.get_id() == 'cython'), None)
-            if cython_compiler is not None and mesonlib.version_compare(cython_compiler.version, '< 3.0.0'):
-                mlog.warning(f'Limited API not supported by Cython versions < 3.0.0 (detected: {cython_compiler.version})', location=self.current_node)
+            if cython_compiler is not None:
+                # Determine if any of the supplied source files are Cython source.
+                def has_cython_files(cython_compiler, args):
+                    cython_suffixes = cython_compiler.file_suffixes
+                    for arg in args:
+                        if isinstance(arg, mesonlib.File):
+                            arg = arg.fname
+                        suffix = os.path.splitext(arg)[1][1:].lower()
+                        if suffix in cython_suffixes:
+                            return True
+                    return False
+
+                # Cython's support for the Limited API was added in version 3.0
+                def has_cython_limited_api(cython_compiler):
+                    return mesonlib.version_compare(cython_compiler.version, '>= 3.0.0')
+
+                if has_cython_files(cython_compiler, args[1]) and not has_cython_limited_api(cython_compiler):
+                    mlog.error(f'Limited API not supported by Cython versions < 3.0.0 (detected: {cython_compiler.version})', location=self.current_node)
 
         kwargs['dependencies'] = new_deps