diff --git a/packages/eslint-plugin/src/rules/quotes.ts b/packages/eslint-plugin/src/rules/quotes.ts
index a266e912fdf..5d4d44028b1 100644
--- a/packages/eslint-plugin/src/rules/quotes.ts
+++ b/packages/eslint-plugin/src/rules/quotes.ts
@@ -42,6 +42,7 @@ export default util.createRule<Options, MessageIds>({
         case AST_NODE_TYPES.TSPropertySignature:
         case AST_NODE_TYPES.TSModuleDeclaration:
         case AST_NODE_TYPES.TSLiteralType:
+        case AST_NODE_TYPES.TSExternalModuleReference:
           return true;
 
         case AST_NODE_TYPES.TSEnumMember:
diff --git a/packages/eslint-plugin/tests/rules/quotes.test.ts b/packages/eslint-plugin/tests/rules/quotes.test.ts
index c6bf01f3e77..ad1487b8506 100644
--- a/packages/eslint-plugin/tests/rules/quotes.test.ts
+++ b/packages/eslint-plugin/tests/rules/quotes.test.ts
@@ -310,7 +310,11 @@ ruleTester.run('quotes', rule, {
       code: `export * from "a"; export * from 'b';`,
       options: ['backtick'],
     },
-
+    // `backtick` should not warn import with require.
+    {
+      code: `import moment = require('moment');`,
+      options: ['backtick'],
+    },
     // `backtick` should not warn property/method names (not computed).
     {
       code: `var obj = {"key0": 0, 'key1': 1};`,