diff --git a/mesonpy/__init__.py b/mesonpy/__init__.py
index 05016a1c3..698719290 100644
--- a/mesonpy/__init__.py
+++ b/mesonpy/__init__.py
@@ -940,10 +940,22 @@ def _project(config_settings: Optional[Dict[Any, Any]] = None) -> Iterator[Proje
     build_dir = settings.get('build-dir')
     editable_verbose = bool(settings.get('editable-verbose'))
 
-    with contextlib.ExitStack() as ctx:
-        if build_dir is None:
-            build_dir = ctx.enter_context(tempfile.TemporaryDirectory(prefix='.mesonpy-', dir=source_dir))
-        yield Project(source_dir, build_dir, meson_args, editable_verbose)
+    try:
+        with contextlib.ExitStack() as ctx:
+            if build_dir is None:
+                build_dir = ctx.enter_context(tempfile.TemporaryDirectory(
+                    prefix='.mesonpy-', dir=source_dir))
+            yield Project(source_dir, build_dir, meson_args, editable_verbose)
+    except PermissionError as exc:
+        # Cleanup may fail on Windows due to background processes (gh-559)
+        str_err = str(exc)
+        if '[WinError 32]' in str_err:
+            prefix = f'{style.ERROR}meson-python: warning:{style.RESET} '
+            str_err = '\n'.join([str_err,
+                'Clean up build directory manually, if desired.'])
+            _log('\n' + textwrap.indent(str_err, prefix))
+        else:
+            raise RuntimeError from exc
 
 
 def _parse_version_string(string: str) -> Tuple[int, ...]: