diff --git a/lib/rules/require-typed-ref.js b/lib/rules/require-typed-ref.js
index 60a82432a..c05e6c829 100644
--- a/lib/rules/require-typed-ref.js
+++ b/lib/rules/require-typed-ref.js
@@ -44,13 +44,23 @@ module.exports = {
       return {}
     }
 
-    const scriptSetup = utils.getScriptSetupElement(context)
-    if (
-      scriptSetup &&
-      !utils.hasAttribute(scriptSetup, 'lang', 'ts') &&
-      !utils.hasAttribute(scriptSetup, 'lang', 'typescript')
-    ) {
-      return {}
+    if (utils.isVueFile(filename)) {
+      const sourceCode = context.getSourceCode()
+      const documentFragment =
+        sourceCode.parserServices.getDocumentFragment &&
+        sourceCode.parserServices.getDocumentFragment()
+      if (!documentFragment) {
+        return {}
+      }
+      const scripts = documentFragment.children.filter(
+        /** @returns {element is VElement} */
+        (element) => utils.isVElement(element) && element.name === 'script'
+      )
+      if (
+        scripts.every((script) => !utils.hasAttribute(script, 'lang', 'ts'))
+      ) {
+        return {}
+      }
     }
 
     const defines = iterateDefineRefs(
diff --git a/tests/lib/rules/require-typed-ref.js b/tests/lib/rules/require-typed-ref.js
index 6e8797943..5b18bcb3c 100644
--- a/tests/lib/rules/require-typed-ref.js
+++ b/tests/lib/rules/require-typed-ref.js
@@ -86,6 +86,20 @@ tester.run('require-typed-ref', rule, {
       `,
       languageOptions: { parser: require('vue-eslint-parser') }
     },
+    {
+      filename: 'test.vue',
+      code: `
+        <script>
+          import { ref } from 'vue'
+          export default {
+            setup() {
+              const count = ref()
+            }
+          }
+        </script>
+      `,
+      languageOptions: { parser: require('vue-eslint-parser') }
+    },
     {
       filename: 'test.js',
       code: `
@@ -217,6 +231,30 @@ tester.run('require-typed-ref', rule, {
       ],
       languageOptions: { parser: require('vue-eslint-parser') }
     },
+    {
+      filename: 'test.vue',
+      code: `
+        <script lang="ts">
+          import { ref } from 'vue'
+          export default {
+            setup() {
+              const count = ref()
+            }
+          }
+        </script>
+      }
+      `,
+      errors: [
+        {
+          messageId: 'noType',
+          line: 6,
+          column: 29,
+          endLine: 6,
+          endColumn: 34
+        }
+      ],
+      languageOptions: { parser: require('vue-eslint-parser') }
+    },
     {
       filename: 'test.ts',
       code: `