diff --git a/docs/rules/throw-new-error.md b/docs/rules/throw-new-error.md
index 96f8f5a1ee..902226b8fd 100644
--- a/docs/rules/throw-new-error.md
+++ b/docs/rules/throw-new-error.md
@@ -4,18 +4,30 @@ While it's possible to create a new error without using the `new` keyword, it's
 
 This rule is fixable.
 
-
 ## Fail
 
 ```js
 throw Error();
+```
+
+```js
 throw TypeError('unicorn');
 ```
 
+```js
+throw lib.TypeError();
+```
 
 ## Pass
 
 ```js
 throw new Error();
+```
+
+```js
 throw new TypeError('unicorn');
 ```
+
+```js
+throw new lib.TypeError();
+```
diff --git a/rules/throw-new-error.js b/rules/throw-new-error.js
index 4684ef2abc..47437911b8 100644
--- a/rules/throw-new-error.js
+++ b/rules/throw-new-error.js
@@ -1,24 +1,38 @@
 'use strict';
 const getDocumentationUrl = require('./utils/get-documentation-url');
 
+const messageId = 'throw-new-error';
+const customError = /^(?:[A-Z][\da-z]*)*Error$/;
+
 const selector = [
 	'ThrowStatement',
 	'>',
-	'CallExpression',
-	'[callee.type="Identifier"]'
+	'CallExpression.argument',
+	`:matches(${
+		[
+			// `throw FooError()`
+			[
+				'[callee.type="Identifier"]',
+				`[callee.name=/${customError.source}/]`
+			],
+			// `throw lib.FooError()`
+			[
+				'[callee.type="MemberExpression"]',
+				'[callee.computed=false]',
+				'[callee.property.type="Identifier"]',
+				`[callee.property.name=/${customError.source}/]`
+			]
+		].map(selector => selector.join('')).join(', ')
+	})`
 ].join('');
-const customError = /^(?:[A-Z][\da-z]*)*Error$/;
-const message = 'Use `new` when throwing an error.';
 
 const create = context => ({
 	[selector]: node => {
-		if (customError.test(node.callee.name)) {
-			context.report({
-				node,
-				message,
-				fix: fixer => fixer.insertTextBefore(node, 'new ')
-			});
-		}
+		context.report({
+			node,
+			messageId,
+			fix: fixer => fixer.insertTextBefore(node, 'new ')
+		});
 	}
 });
 
@@ -29,6 +43,9 @@ module.exports = {
 		docs: {
 			url: getDocumentationUrl(__filename)
 		},
+		messages: {
+			[messageId]: 'Use `new` when throwing an error.'
+		},
 		fixable: 'code'
 	}
 };
diff --git a/test/throw-new-error.js b/test/throw-new-error.js
index 728d5bd3a1..6addf91f45 100644
--- a/test/throw-new-error.js
+++ b/test/throw-new-error.js
@@ -2,13 +2,15 @@ import test from 'ava';
 import avaRuleTester from 'eslint-ava-rule-tester';
 import rule from '../rules/throw-new-error';
 
+const messageId = 'throw-new-error';
+
 const ruleTester = avaRuleTester(test, {
-	env: {
-		es6: true
+	parserOptions: {
+		ecmaVersion: 2020
 	}
 });
 
-const errors = [{ruleId: 'throw-new-error'}];
+const errors = [{messageId}];
 
 ruleTester.run('new-error', rule, {
 	valid: [
@@ -28,8 +30,14 @@ ruleTester.run('new-error', rule, {
 		'throw getError()',
 		// Not `CallExpression`
 		'throw CustomError',
-		// Not `Identifier`
-		'throw lib.Error()'
+		// Not `Identifier` / `MemberExpression`
+		'throw getErrorConstructor()()',
+		// `MemberExpression.computed`
+		'throw lib[Error]()',
+		// `MemberExpression.property` not `Identifier`
+		'throw lib["Error"]()',
+		// Not `FooError` like
+		'throw lib.getError()'
 	],
 	invalid: [
 		{
@@ -37,6 +45,31 @@ ruleTester.run('new-error', rule, {
 			output: 'throw new Error()',
 			errors
 		},
+		{
+			code: 'throw (Error)()',
+			output: 'throw new (Error)()',
+			errors
+		},
+		{
+			code: 'throw lib.Error()',
+			output: 'throw new lib.Error()',
+			errors
+		},
+		{
+			code: 'throw lib.mod.Error()',
+			output: 'throw new lib.mod.Error()',
+			errors
+		},
+		{
+			code: 'throw lib[mod].Error()',
+			output: 'throw new lib[mod].Error()',
+			errors
+		},
+		{
+			code: 'throw (lib.mod).Error()',
+			output: 'throw new (lib.mod).Error()',
+			errors
+		},
 		{
 			code: 'throw Error(\'foo\')',
 			output: 'throw new Error(\'foo\')',