diff --git a/CHANGELOG.md b/CHANGELOG.md
index 92f79ba66b72..10f2f668712b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -9,6 +9,7 @@
 ### Fixes
 
 - `[expect]` Allow again `expect.Matchers` generic with single value ([#11986](https://github.com/facebook/jest/pull/11986))
+- `[jest-circus, jest-jasmine2]` Avoid false concurrent test failures due to unhandled promise rejections ([#11987](https://github.com/facebook/jest/pull/11987))
 - `[jest-config]` Add missing `slash` dependency to `package.json` ([#12080](https://github.com/facebook/jest/pull/12080))
 - `[jest-core]` Incorrect detection of open ZLIB handles ([#12022](https://github.com/facebook/jest/pull/12022))
 - `[jest-diff]` Break dependency cycle ([#10818](https://github.com/facebook/jest/pull/10818))
diff --git a/e2e/__tests__/jasmineAsync.test.ts b/e2e/__tests__/jasmineAsync.test.ts
index 3006a04b3810..8b6cfb93ec1c 100644
--- a/e2e/__tests__/jasmineAsync.test.ts
+++ b/e2e/__tests__/jasmineAsync.test.ts
@@ -168,4 +168,13 @@ describe('async jasmine', () => {
 
     expect(result.exitCode).toBe(0);
   });
+
+  it('works when another test fails while one is running', () => {
+    const {json} = runWithJson('jasmine-async', [
+      'concurrent-parallel-failure.test.js',
+    ]);
+    expect(json.numTotalTests).toBe(2);
+    expect(json.numPassedTests).toBe(1);
+    expect(json.numFailedTests).toBe(1);
+  });
 });
diff --git a/e2e/jasmine-async/__tests__/concurrent-parallel-failure.test.js b/e2e/jasmine-async/__tests__/concurrent-parallel-failure.test.js
new file mode 100644
index 000000000000..e4869be91465
--- /dev/null
+++ b/e2e/jasmine-async/__tests__/concurrent-parallel-failure.test.js
@@ -0,0 +1,16 @@
+/**
+ * Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
+ *
+ * This source code is licensed under the MIT license found in the
+ * LICENSE file in the root directory of this source tree.
+ */
+
+'use strict';
+
+it.concurrent('Good Test', async () => {
+  await new Promise(r => setTimeout(r, 100));
+});
+
+it.concurrent('Bad Test', async () => {
+  expect('a').toBe('b');
+});
diff --git a/packages/jest-circus/src/legacy-code-todo-rewrite/jestAdapterInit.ts b/packages/jest-circus/src/legacy-code-todo-rewrite/jestAdapterInit.ts
index d7487477e31d..43bf59f1af4e 100644
--- a/packages/jest-circus/src/legacy-code-todo-rewrite/jestAdapterInit.ts
+++ b/packages/jest-circus/src/legacy-code-todo-rewrite/jestAdapterInit.ts
@@ -93,6 +93,9 @@ export const initialize = async ({
       // that will result in this test to be skipped, so we'll be executing the promise function anyway,
       // even if it ends up being skipped.
       const promise = mutex(() => testFn());
+      // Avoid triggering the uncaught promise rejection handler in case the test errors before
+      // being awaited on.
+      promise.catch(() => {});
       globalsObject.test(testName, () => promise, timeout);
     };
 
diff --git a/packages/jest-jasmine2/src/jasmineAsyncInstall.ts b/packages/jest-jasmine2/src/jasmineAsyncInstall.ts
index 6a31a66c32b7..84836e81dba4 100644
--- a/packages/jest-jasmine2/src/jasmineAsyncInstall.ts
+++ b/packages/jest-jasmine2/src/jasmineAsyncInstall.ts
@@ -215,6 +215,9 @@ function makeConcurrent(
     } catch (error: unknown) {
       promise = Promise.reject(error);
     }
+    // Avoid triggering the uncaught promise rejection handler in case the test errors before
+    // being awaited on.
+    promise.catch(() => {});
 
     return spec;
   };