diff --git a/packages/eslint-plugin/src/rules/sort-interface-members.ts b/packages/eslint-plugin/src/rules/sort-interface-members.ts
new file mode 100644
index 000000000000..7d7c53a8cd79
--- /dev/null
+++ b/packages/eslint-plugin/src/rules/sort-interface-members.ts
@@ -0,0 +1,199 @@
+/**
+ * @fileoverview Forbids unsorted interface members
+ */
+
+import * as util from '../util';
+import { AST_NODE_TYPES, TSESTree } from '@typescript-eslint/typescript-estree';
+
+type Options = [];
+type MessageIds = 'notSorted';
+
+function isPropertySignature(
+  member: TSESTree.TypeElement,
+): member is TSESTree.TSPropertySignature {
+  return member.type === AST_NODE_TYPES.TSPropertySignature;
+}
+
+function isMethodSignature(
+  member: TSESTree.TypeElement,
+): member is TSESTree.TSMethodSignature {
+  return member.type === AST_NODE_TYPES.TSMethodSignature;
+}
+
+function isIndexSignature(
+  member: TSESTree.TypeElement,
+): member is TSESTree.TSIndexSignature {
+  return member.type === AST_NODE_TYPES.TSIndexSignature;
+}
+
+function isConstructSignatureDeclaration(
+  member: TSESTree.TypeElement,
+): member is TSESTree.TSConstructSignatureDeclaration {
+  return member.type === AST_NODE_TYPES.TSConstructSignatureDeclaration;
+}
+
+function isCallSignatureDeclaration(
+  member: TSESTree.TypeElement,
+): member is TSESTree.TSCallSignatureDeclaration {
+  return member.type === AST_NODE_TYPES.TSCallSignatureDeclaration;
+}
+
+export default util.createRule<Options, MessageIds>({
+  name: 'sort-interface-members',
+  meta: {
+    type: 'suggestion',
+    docs: {
+      description: 'Forbids unsorted interface members',
+      category: 'Stylistic Issues',
+      recommended: false,
+    },
+    schema: [],
+    messages: {
+      notSorted: 'The interface members are not sorted alphabetically.',
+    },
+  },
+  defaultOptions: [],
+  create(context) {
+    return {
+      TSInterfaceBody(node) {
+        const members = node.body;
+        const propertySignatures: TSESTree.TSPropertySignature[] = [];
+        const methodSignatures: TSESTree.TSMethodSignature[] = [];
+        const indexSignatures: TSESTree.TSIndexSignature[] = [];
+        const constructSignatureDeclarations: TSESTree.TSConstructSignatureDeclaration[] = [];
+        const callSignatureDeclarations: TSESTree.TSCallSignatureDeclaration[] = [];
+
+        // TODO This algorithm assumes an order of TSESTree.TSPropertySignature > TSMethodSignature > TSIndexSignature > TSConstructSignatureDeclaration > TSCallSignatureDeclaration - it is only used to evaluate if it works alongside the member-ordering rule
+        for (let i = 0; i < members.length; i++) {
+          if (isPropertySignature(members[i])) {
+            if (
+              methodSignatures.length > 0 ||
+              indexSignatures.length > 0 ||
+              constructSignatureDeclarations.length > 0 ||
+              callSignatureDeclarations.length > 0
+            ) {
+              return context.report({
+                messageId: 'notSorted',
+                node: members[i],
+              });
+            }
+
+            propertySignatures.push(members[i] as TSESTree.TSPropertySignature);
+          } else if (isMethodSignature(members[i])) {
+            if (
+              indexSignatures.length > 0 ||
+              constructSignatureDeclarations.length > 0 ||
+              callSignatureDeclarations.length > 0
+            ) {
+              return context.report({
+                messageId: 'notSorted',
+                node: members[i],
+              });
+            }
+
+            methodSignatures.push(members[i] as TSESTree.TSMethodSignature);
+          } else if (isIndexSignature(members[i])) {
+            if (
+              constructSignatureDeclarations.length > 0 ||
+              callSignatureDeclarations.length > 0
+            ) {
+              return context.report({
+                messageId: 'notSorted',
+                node: members[i],
+              });
+            }
+
+            indexSignatures.push(members[i] as TSESTree.TSIndexSignature);
+          } else if (isConstructSignatureDeclaration(members[i])) {
+            if (callSignatureDeclarations.length > 0) {
+              return context.report({
+                messageId: 'notSorted',
+                node: members[i],
+              });
+            }
+
+            constructSignatureDeclarations.push(members[
+              i
+            ] as TSESTree.TSConstructSignatureDeclaration);
+          } else if (isCallSignatureDeclaration(members[i])) {
+            callSignatureDeclarations.push(members[
+              i
+            ] as TSESTree.TSCallSignatureDeclaration);
+          }
+        }
+
+        for (let i = 0; i < propertySignatures.length - 1; i++) {
+          const currentItem = propertySignatures[i].key as TSESTree.Identifier;
+          const nextItem = propertySignatures[i + 1].key as TSESTree.Identifier;
+
+          if (currentItem.name > nextItem.name) {
+            return context.report({
+              messageId: 'notSorted',
+              node: currentItem,
+            });
+          }
+        }
+
+        for (let i = 0; i < methodSignatures.length - 1; i++) {
+          const currentItem = methodSignatures[i].key as TSESTree.Identifier;
+          const nextItem = methodSignatures[i + 1].key as TSESTree.Identifier;
+
+          if (currentItem.name > nextItem.name) {
+            return context.report({
+              messageId: 'notSorted',
+              node: currentItem,
+            });
+          }
+        }
+
+        for (let i = 0; i < indexSignatures.length - 1; i++) {
+          const currentItem = indexSignatures[i]
+            .parameters[0] as TSESTree.Identifier;
+          const nextItem = indexSignatures[i + 1]
+            .parameters[0] as TSESTree.Identifier;
+
+          if (currentItem.name > nextItem.name) {
+            return context.report({
+              messageId: 'notSorted',
+              node: currentItem,
+            });
+          }
+        }
+
+        for (let i = 0; i < constructSignatureDeclarations.length - 1; i++) {
+          const currentItem = ((constructSignatureDeclarations[i]
+            .returnType as TSESTree.TSTypeAnnotation)
+            .typeAnnotation as TSESTree.TSTypeReference).typeName;
+          const nextItem = ((constructSignatureDeclarations[i + 1]
+            .returnType as TSESTree.TSTypeAnnotation)
+            .typeAnnotation as TSESTree.TSTypeReference).typeName;
+
+          if (currentItem > nextItem) {
+            return context.report({
+              messageId: 'notSorted',
+              node: currentItem,
+            });
+          }
+        }
+
+        for (let i = 0; i < callSignatureDeclarations.length - 1; i++) {
+          const currentItem = ((callSignatureDeclarations[i]
+            .returnType as TSESTree.TSTypeAnnotation)
+            .typeAnnotation as TSESTree.TSTypeReference).typeName;
+          const nextItem = ((callSignatureDeclarations[i + 1]
+            .returnType as TSESTree.TSTypeAnnotation)
+            .typeAnnotation as TSESTree.TSTypeReference).typeName;
+
+          if (currentItem > nextItem) {
+            return context.report({
+              messageId: 'notSorted',
+              node: currentItem,
+            });
+          }
+        }
+
+        return; // No rule violation found
+      },
+    };
+  },
+});
diff --git a/packages/eslint-plugin/tests/rules/sort-interface-members.test.ts b/packages/eslint-plugin/tests/rules/sort-interface-members.test.ts
new file mode 100644
index 000000000000..4a45ee31f2b6
--- /dev/null
+++ b/packages/eslint-plugin/tests/rules/sort-interface-members.test.ts
@@ -0,0 +1,80 @@
+import { RuleTester } from '../RuleTester';
+import rule from '../../src/rules/sort-interface-members';
+
+const ruleTester = new RuleTester({
+  parser: '@typescript-eslint/parser',
+});
+
+// TODO Add tests for lowercase/uppercase letters
+// TODO Add tests for special characters
+// TODO Add tests for the order of the groups
+// TODO Add tests for the order inside of the groups
+ruleTester.run('sort-interface-members', rule, {
+  valid: [
+    `
+interface Foo {
+  a : string;
+  a() : string;
+  [a: string]: string;
+  new () : A;
+  () : A;
+}
+    `,
+    `
+interface Foo {
+  a : string;
+  a : string;
+  a() : string;
+  a() : string;
+  [a: string]: string;
+  [a: string]: string;
+  new () : A;
+  new () : A;
+  () : A;
+  () : A;
+}
+    `,
+    `
+interface Foo {
+  a : string;
+  b : string;
+  a() : string;
+  b() : string;
+  [a: string]: string;
+  [b: string]: string;
+  new () : A;
+  new () : B;
+  () : A;
+  () : B;
+}
+    `,
+  ],
+  invalid: [
+    {
+      code: `
+interface Foo {
+  a() : string;
+  a : string;
+}
+    `,
+      errors: [
+        {
+          messageId: 'notSorted',
+        },
+      ],
+    },
+    {
+      code: `
+interface Foo {
+  b : string;
+  a : string;
+}
+    `,
+      errors: [
+        {
+          messageId: 'notSorted',
+        },
+      ],
+    },
+  ],
+});