diff --git a/lib/_stream_readable.js b/lib/_stream_readable.js
index 49981b47e04aa8..17f433f03d939d 100644
--- a/lib/_stream_readable.js
+++ b/lib/_stream_readable.js
@@ -284,7 +284,8 @@ function readableAddChunk(stream, chunk, encoding, addToFront) {
 }
 
 function addChunk(stream, state, chunk, addToFront) {
-  if (state.flowing && state.length === 0 && !state.sync) {
+  if (state.flowing && state.length === 0 && !state.sync &&
+      stream.listenerCount('data') > 0) {
     // Use the guard to avoid creating `Set()` repeatedly
     // when we have multiple pipes.
     if (state.multiAwaitDrain) {
diff --git a/test/parallel/test-stream-readable-add-chunk-during-data.js b/test/parallel/test-stream-readable-add-chunk-during-data.js
new file mode 100644
index 00000000000000..6c36359790633e
--- /dev/null
+++ b/test/parallel/test-stream-readable-add-chunk-during-data.js
@@ -0,0 +1,21 @@
+'use strict';
+const common = require('../common');
+const assert = require('assert');
+const { Readable } = require('stream');
+
+// Verify that .push() and .unshift() can be called from 'data' listeners.
+
+for (const method of ['push', 'unshift']) {
+  const r = new Readable({ read() {} });
+  r.once('data', common.mustCall((chunk) => {
+    assert.strictEqual(r.readableLength, 0);
+    r[method](chunk);
+    assert.strictEqual(r.readableLength, chunk.length);
+
+    r.on('data', common.mustCall((chunk) => {
+      assert.strictEqual(chunk.toString(), 'Hello, world');
+    }));
+  }));
+
+  r.push('Hello, world');
+}