diff --git a/packages/eslint-plugin/src/rules/member-ordering.ts b/packages/eslint-plugin/src/rules/member-ordering.ts
index 29b748e88cf..f7ad60c58fe 100644
--- a/packages/eslint-plugin/src/rules/member-ordering.ts
+++ b/packages/eslint-plugin/src/rules/member-ordering.ts
@@ -800,6 +800,10 @@ export default util.createRule<Options, MessageIds>({
       previousName: string,
       order: AlphabeticalOrder,
     ): boolean {
+      if (name === previousName) {
+        return false;
+      }
+
       switch (order) {
         case 'alphabetically':
           return name < previousName;
diff --git a/packages/eslint-plugin/tests/rules/member-ordering.test.ts b/packages/eslint-plugin/tests/rules/member-ordering.test.ts
index 9e8dda8b778..b947d8a5a1e 100644
--- a/packages/eslint-plugin/tests/rules/member-ordering.test.ts
+++ b/packages/eslint-plugin/tests/rules/member-ordering.test.ts
@@ -2008,6 +2008,53 @@ interface Foo {
         },
       ],
     },
+    // https://github.com/typescript-eslint/typescript-eslint/issues/6812
+    {
+      code: `
+class Foo {
+  #bar: string;
+
+  get bar(): string {
+    return this.#bar;
+  }
+
+  set bar(value: string) {
+    this.#bar = value;
+  }
+}
+      `,
+      options: [
+        {
+          default: {
+            memberTypes: [['get', 'set']],
+            order: 'alphabetically',
+          },
+        },
+      ],
+    },
+    {
+      code: `
+class Foo {
+  #bar: string;
+
+  get bar(): string {
+    return this.#bar;
+  }
+
+  set bar(value: string) {
+    this.#bar = value;
+  }
+}
+      `,
+      options: [
+        {
+          default: {
+            memberTypes: [['get', 'set']],
+            order: 'natural',
+          },
+        },
+      ],
+    },
   ],
   invalid: [
     {