diff --git a/packages/eslint-plugin/src/rules/consistent-generic-constructors.ts b/packages/eslint-plugin/src/rules/consistent-generic-constructors.ts
index 0df1412bd7b..db95efa9a57 100644
--- a/packages/eslint-plugin/src/rules/consistent-generic-constructors.ts
+++ b/packages/eslint-plugin/src/rules/consistent-generic-constructors.ts
@@ -1,4 +1,4 @@
-import { AST_NODE_TYPES } from '@typescript-eslint/utils';
+import { AST_NODE_TYPES, TSESTree } from '@typescript-eslint/utils';
 import { createRule } from '../util';
 
 type MessageIds = 'preferTypeAnnotation' | 'preferConstructor';
@@ -30,9 +30,16 @@ export default createRule<Options, MessageIds>({
   create(context, [mode]) {
     const sourceCode = context.getSourceCode();
     return {
-      VariableDeclarator(node): void {
-        const lhs = node.id.typeAnnotation?.typeAnnotation;
-        const rhs = node.init;
+      'VariableDeclarator,PropertyDefinition'(
+        node: TSESTree.VariableDeclarator | TSESTree.PropertyDefinition,
+      ): void {
+        const lhs = (
+          node.type === AST_NODE_TYPES.VariableDeclarator ? node.id : node
+        ).typeAnnotation?.typeAnnotation;
+        const rhs =
+          node.type === AST_NODE_TYPES.VariableDeclarator
+            ? node.init
+            : node.value;
         if (
           !rhs ||
           rhs.type !== AST_NODE_TYPES.NewExpression ||
@@ -57,9 +64,25 @@ export default createRule<Options, MessageIds>({
               node,
               messageId: 'preferTypeAnnotation',
               fix(fixer) {
+                function getIDToAttachAnnotation():
+                  | TSESTree.Token
+                  | TSESTree.Node {
+                  if (node.type === AST_NODE_TYPES.VariableDeclarator) {
+                    return node.id;
+                  }
+                  if (!node.computed) {
+                    return node.key;
+                  }
+                  // If the property's computed, we have to attach the
+                  // annotation after the square bracket, not the enclosed expression
+                  return sourceCode.getTokenAfter(node.key)!;
+                }
                 return [
                   fixer.remove(typeParameters),
-                  fixer.insertTextAfter(node.id, ': ' + typeAnnotation),
+                  fixer.insertTextAfter(
+                    getIDToAttachAnnotation(),
+                    ': ' + typeAnnotation,
+                  ),
                 ];
               },
             });
diff --git a/packages/eslint-plugin/tests/rules/consistent-generic-constructors.test.ts b/packages/eslint-plugin/tests/rules/consistent-generic-constructors.test.ts
index 0fe3bcae7fb..bdfb68e2788 100644
--- a/packages/eslint-plugin/tests/rules/consistent-generic-constructors.test.ts
+++ b/packages/eslint-plugin/tests/rules/consistent-generic-constructors.test.ts
@@ -19,6 +19,11 @@ ruleTester.run('consistent-generic-constructors', rule, {
     'const a: Foo<string> = Foo<string>();',
     'const a: Foo<string> = Foo();',
     'const a: Foo = Foo<string>();',
+    `
+class Foo {
+  a = new Foo<string>();
+}
+    `,
     // type-annotation
     {
       code: 'const a = new Foo();',
@@ -60,6 +65,14 @@ ruleTester.run('consistent-generic-constructors', rule, {
       code: 'const a = new (class C<T> {})<string>();',
       options: ['type-annotation'],
     },
+    {
+      code: `
+class Foo {
+  a: Foo<string> = new Foo();
+}
+      `,
+      options: ['type-annotation'],
+    },
   ],
   invalid: [
     {
@@ -143,6 +156,40 @@ ruleTester.run('consistent-generic-constructors', rule, {
       ],
       output: noFormat`const a = new \n Foo<string> \n ();`,
     },
+    {
+      code: `
+class Foo {
+  a: Foo<string> = new Foo();
+}
+      `,
+      errors: [
+        {
+          messageId: 'preferConstructor',
+        },
+      ],
+      output: `
+class Foo {
+  a = new Foo<string>();
+}
+      `,
+    },
+    {
+      code: `
+class Foo {
+  [a]: Foo<string> = new Foo();
+}
+      `,
+      errors: [
+        {
+          messageId: 'preferConstructor',
+        },
+      ],
+      output: `
+class Foo {
+  [a] = new Foo<string>();
+}
+      `,
+    },
     {
       code: 'const a = new Foo<string>();',
       options: ['type-annotation'],
@@ -213,5 +260,59 @@ ruleTester.run('consistent-generic-constructors', rule, {
       ],
       output: noFormat`const a: Foo</* comment */ string, /* another */ number> = new Foo();`,
     },
+    {
+      code: `
+class Foo {
+  a = new Foo<string>();
+}
+      `,
+      options: ['type-annotation'],
+      errors: [
+        {
+          messageId: 'preferTypeAnnotation',
+        },
+      ],
+      output: `
+class Foo {
+  a: Foo<string> = new Foo();
+}
+      `,
+    },
+    {
+      code: `
+class Foo {
+  [a] = new Foo<string>();
+}
+      `,
+      options: ['type-annotation'],
+      errors: [
+        {
+          messageId: 'preferTypeAnnotation',
+        },
+      ],
+      output: `
+class Foo {
+  [a]: Foo<string> = new Foo();
+}
+      `,
+    },
+    {
+      code: `
+class Foo {
+  [a + b] = new Foo<string>();
+}
+      `,
+      options: ['type-annotation'],
+      errors: [
+        {
+          messageId: 'preferTypeAnnotation',
+        },
+      ],
+      output: `
+class Foo {
+  [a + b]: Foo<string> = new Foo();
+}
+      `,
+    },
   ],
 });