diff --git a/packages/toolpad-app/package.json b/packages/toolpad-app/package.json
index d818e64fc60..e0604e286b4 100644
--- a/packages/toolpad-app/package.json
+++ b/packages/toolpad-app/package.json
@@ -66,6 +66,7 @@
     "json-to-ts": "^1.7.0",
     "json5": "^2.2.1",
     "lodash-es": "^4.17.21",
+    "monaco-editor": "0.34.0-dev.20220725",
     "next": "12.2.0",
     "node-fetch": "^3.2.6",
     "node-fetch-har": "^1.0.1",
@@ -110,7 +111,6 @@
     "eslint-config-prettier": "^8.3.0",
     "eslint-plugin-import": "^2.25.3",
     "glob": "^8.0.3",
-    "monaco-editor": "^0.34.0-dev.20220722",
     "webpack": "^5.73.0"
   },
   "typings": "./index.d.ts",
diff --git a/packages/toolpad-app/src/components/MonacoEditor.tsx b/packages/toolpad-app/src/components/MonacoEditor.tsx
index 45d4d5c1f7e..a6a05ea8f4d 100644
--- a/packages/toolpad-app/src/components/MonacoEditor.tsx
+++ b/packages/toolpad-app/src/components/MonacoEditor.tsx
@@ -10,6 +10,7 @@ import clsx from 'clsx';
 import cuid from 'cuid';
 import invariant from 'invariant';
 import monacoEditorTheme from '../monacoEditorTheme';
+import muiTheme from '../theme';
 
 function getExtension(language: string): string {
   switch (language) {
@@ -107,6 +108,19 @@ const EditorRoot = styled('div')(({ theme }) => ({
   },
 }));
 
+let overflowWidgetsDomNode: HTMLDivElement | null = null;
+function getOverflowWidgetsDomNode(): HTMLDivElement {
+  if (!overflowWidgetsDomNode) {
+    overflowWidgetsDomNode = document.createElement('div');
+    // See https://github.com/microsoft/monaco-editor/issues/2233#issuecomment-913170212
+    overflowWidgetsDomNode.classList.add('monaco-editor');
+    overflowWidgetsDomNode.style.zIndex = String(muiTheme.zIndex.tooltip + 1);
+    document.body.append(overflowWidgetsDomNode);
+  }
+
+  return overflowWidgetsDomNode;
+}
+
 export interface MonacoEditorHandle {
   editor: monaco.editor.IStandaloneCodeEditor;
   monaco: typeof monaco;
@@ -190,6 +204,9 @@ export default React.forwardRef<MonacoEditorHandle, MonacoEditorProps>(function
         tabSize: 2,
         automaticLayout: true,
         theme: monacoEditorTheme,
+        fixedOverflowWidgets: true,
+        // See https://github.com/microsoft/monaco-editor/issues/181
+        overflowWidgetsDomNode: getOverflowWidgetsDomNode(),
         ...extraOptions,
       });
 
diff --git a/yarn.lock b/yarn.lock
index d10296d3bef..cd9036abfbf 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -8954,10 +8954,10 @@ modify-values@^1.0.0:
   resolved "https://registry.yarnpkg.com/modify-values/-/modify-values-1.0.1.tgz#b3939fa605546474e3e3e3c63d64bd43b4ee6022"
   integrity sha512-xV2bxeN6F7oYjZWTe/YPAy6MN2M+sL4u/Rlm2AHCIVGfo2p1yGmBHQ6vHehl4bRTZBdHu3TSkWdYgkwpYzAGSw==
 
-monaco-editor@^0.34.0-dev.20220722:
-  version "0.34.0-dev.20220722"
-  resolved "https://registry.yarnpkg.com/monaco-editor/-/monaco-editor-0.34.0-dev.20220722.tgz#58bbb9477c2790c346c156e80d74585b6691b2e3"
-  integrity sha512-6l2hFsHOJE+5TQFDoWBeoACKcissTeLD5+xJ2HrtvP86sHnpnZy7ffbcFQCKpInJKIBSP7+y/bpctYn8eSAYTQ==
+monaco-editor@0.34.0-dev.20220725:
+  version "0.34.0-dev.20220725"
+  resolved "https://registry.yarnpkg.com/monaco-editor/-/monaco-editor-0.34.0-dev.20220725.tgz#79e6bdef9dd3e1e5a66ebbbef549604064695b22"
+  integrity sha512-MiuJINwVQyqEEieWQ2NEcapjmi2MiAibthhpK2Tj2pd5tMHtZMO2PpoAKQla1cwxfhTlkb7e+cv0a+CN7Cl67A==
 
 mrmime@^1.0.0:
   version "1.0.1"