diff --git a/.changeset/eight-swans-destroy.md b/.changeset/eight-swans-destroy.md
new file mode 100644
index 00000000000..6f56edffaa1
--- /dev/null
+++ b/.changeset/eight-swans-destroy.md
@@ -0,0 +1,5 @@
+---
+'graphql-language-service-server': patch
+---
+
+fix: vue and svelte files doesn't log errors anymore when parsing with no script tag (#2836)
diff --git a/packages/graphql-language-service-server/src/__tests__/findGraphQLTags-test.ts b/packages/graphql-language-service-server/src/__tests__/findGraphQLTags-test.ts
index 48bd37be429..15aac193bb1 100644
--- a/packages/graphql-language-service-server/src/__tests__/findGraphQLTags-test.ts
+++ b/packages/graphql-language-service-server/src/__tests__/findGraphQLTags-test.ts
@@ -289,6 +289,72 @@ query {id}
 query {id}`);
   });
 
+  it('no crash in Svelte files without <script>', async () => {
+    const text = ``;
+
+    const consoleErrorSpy = jest
+      .spyOn(process.stderr, 'write')
+      .mockImplementation(() => true);
+
+    const contents = baseFindGraphQLTags(
+      text,
+      '.svelte',
+      '',
+      new Logger(tmpdir(), false),
+    );
+    // We should have no contents
+    expect(contents).toMatchObject([]);
+
+    // Nothing should be logged as it's a managed error
+    expect(consoleErrorSpy.mock.calls.length).toBe(0);
+
+    consoleErrorSpy.mockRestore();
+  });
+
+  it('no crash in Svelte files with empty <script>', async () => {
+    const text = `<script></script>`;
+
+    const consoleErrorSpy = jest
+      .spyOn(process.stderr, 'write')
+      .mockImplementation(() => true);
+
+    const contents = baseFindGraphQLTags(
+      text,
+      '.svelte',
+      '',
+      new Logger(tmpdir(), false),
+    );
+    // We should have no contents
+    expect(contents).toMatchObject([]);
+
+    // Nothing should be logged as it's a managed error
+    expect(consoleErrorSpy.mock.calls.length).toBe(0);
+
+    consoleErrorSpy.mockRestore();
+  });
+
+  it('no crash in Svelte files with empty <script> (typescript)', async () => {
+    const text = `<script lang="ts"></script>`;
+
+    const consoleErrorSpy = jest
+      .spyOn(process.stderr, 'write')
+      .mockImplementation(() => true);
+
+    const contents = baseFindGraphQLTags(
+      text,
+      '.svelte',
+      '',
+      new Logger(tmpdir(), false),
+    );
+    // We should have no contents
+    expect(contents).toMatchObject([]);
+
+    // Nothing should be logged as it's a managed error
+    expect(consoleErrorSpy.mock.calls.length).toBe(0);
+
+    consoleErrorSpy.mockRestore();
+  });
+
   it('finds multiple queries in a single file', async () => {
     const text = `something({
   else: () => gql\` query {} \`
diff --git a/packages/graphql-language-service-server/src/findGraphQLTags.ts b/packages/graphql-language-service-server/src/findGraphQLTags.ts
index a73c757d4b5..5dfd5db8894 100644
--- a/packages/graphql-language-service-server/src/findGraphQLTags.ts
+++ b/packages/graphql-language-service-server/src/findGraphQLTags.ts
@@ -90,6 +90,16 @@ function parseVueSFC(source: string): ParseVueSFCResult {
   try {
     scriptBlock = VueParser.compileScript(descriptor, { id: 'foobar' });
   } catch (error) {
+    if (
+      error instanceof Error &&
+      error.message === '[@vue/compiler-sfc] SFC contains no <script> tags.'
+    ) {
+      return {
+        type: 'ok',
+        scriptSetupAst: [],
+        scriptAst: [],
+      };
+    }
     return { type: 'error', errors: [error as Error] };
   }
 
@@ -118,7 +128,7 @@ export function findGraphQLTags(
     const parseVueSFCResult = parseVueSFC(text);
     if (parseVueSFCResult.type === 'error') {
       logger.error(
-        `Could not parse the Vue file at ${uri} to extract the graphql tags:`,
+        `Could not parse the "${ext}" file at ${uri} to extract the graphql tags:`,
       );
       for (const error of parseVueSFCResult.errors) {
         logger.error(String(error));