diff --git a/lib/internal/worker.js b/lib/internal/worker.js
index 88580893cdc015..669a86bb23faef 100644
--- a/lib/internal/worker.js
+++ b/lib/internal/worker.js
@@ -317,6 +317,7 @@ class Worker extends EventEmitter {
   [kOnExit](code) {
     debug(`[${threadId}] hears end event for Worker ${this.threadId}`);
     MessagePortPrototype.drain.call(this[kPublicPort]);
+    MessagePortPrototype.drain.call(this[kPort]);
     this[kDispose]();
     this.emit('exit', code);
     this.removeAllListeners();
diff --git a/test/parallel/test-worker-message-port-drain.js b/test/parallel/test-worker-message-port-drain.js
new file mode 100644
index 00000000000000..4fcb3da25e3f14
--- /dev/null
+++ b/test/parallel/test-worker-message-port-drain.js
@@ -0,0 +1,41 @@
+// Flags: --experimental-worker
+'use strict';
+require('../common');
+
+// This test ensures that the messages from the internal
+// message port are drained before the call to 'kDispose',
+// and so all the stdio messages from the worker are processed
+// in the parent and are pushed to their target streams.
+
+const assert = require('assert');
+const {
+  Worker,
+  isMainThread,
+  parentPort,
+  threadId,
+} = require('worker_threads');
+
+if (isMainThread) {
+  const workerIdsToOutput = new Map();
+
+  for (let i = 0; i < 2; i++) {
+    const worker = new Worker(__filename, { stdout: true });
+    const workerOutput = [];
+    workerIdsToOutput.set(worker.threadId, workerOutput);
+    worker.on('message', console.log);
+    worker.stdout.on('data', (chunk) => {
+      workerOutput.push(chunk.toString().trim());
+    });
+  }
+
+  process.on('exit', () => {
+    for (const [threadId, workerOutput] of workerIdsToOutput) {
+      assert.ok(workerOutput.includes(`1 threadId: ${threadId}`));
+      assert.ok(workerOutput.includes(`2 threadId: ${threadId}`));
+    }
+  });
+} else {
+  console.log(`1 threadId: ${threadId}`);
+  console.log(`2 threadId: ${threadId}`);
+  parentPort.postMessage(Array(100).fill(1));
+}