diff --git a/lib/rules/multi-word-component-names.js b/lib/rules/multi-word-component-names.js
index 4e4e7db28..6f73de294 100644
--- a/lib/rules/multi-word-component-names.js
+++ b/lib/rules/multi-word-component-names.js
@@ -60,7 +60,7 @@ module.exports = {
         ignores.add(casing.kebabCase(ignore))
       }
     }
-    let hasVue = false
+    let hasVue = utils.isScriptSetup(context)
     let hasName = false
 
     /**
diff --git a/tests/lib/rules/multi-word-component-names.js b/tests/lib/rules/multi-word-component-names.js
index bb0fba770..d11b11d3f 100644
--- a/tests/lib/rules/multi-word-component-names.js
+++ b/tests/lib/rules/multi-word-component-names.js
@@ -202,6 +202,17 @@ tester.run('multi-word-component-names', rule, {
           },
       }).$mount('#app')
       `
+    },
+    {
+      filename: 'MultiWord.vue',
+      code: `
+      <template>
+        <AppButton />
+      </template>
+      
+      <script setup lang="ts">
+      import AppButton from "@/components/AppButton.vue";
+      </script>`
     }
   ],
   invalid: [
@@ -309,6 +320,19 @@ tester.run('multi-word-component-names', rule, {
           line: 4
         }
       ]
+    },
+    {
+      filename: 'test.vue',
+      code: `
+      <script setup lang="ts">
+      import Item from "@/components/Item.vue";
+      </script>`,
+      errors: [
+        {
+          message: 'Component name "test" should always be multi-word.',
+          line: 1
+        }
+      ]
     }
   ]
 })