diff --git a/lib/assert.js b/lib/assert.js
index b4de551e28..7fc9e0c342 100644
--- a/lib/assert.js
+++ b/lib/assert.js
@@ -330,7 +330,14 @@ function _throws(shouldThrow, block, expected, message) {
     fail(actual, expected, 'Missing expected exception' + message);
   }
 
-  if (!shouldThrow && expectedException(actual, expected)) {
+  const userProvidedMessage = typeof message === 'string';
+  const isUnwantedException = !shouldThrow && util.isError(actual);
+  const isUnexpectedException = !shouldThrow && actual && !expected;
+
+  if ((isUnwantedException &&
+      userProvidedMessage &&
+      expectedException(actual, expected)) ||
+      isUnexpectedException) {
     fail(actual, expected, 'Got unwanted exception' + message);
   }
 
diff --git a/test/parallel/test-assert.js b/test/parallel/test-assert.js
index 2f4b757f4e..e537bc3c1d 100644
--- a/test/parallel/test-assert.js
+++ b/test/parallel/test-assert.js
@@ -321,6 +321,11 @@ assert.throws(function() {assert.ifError(new Error('test error'));});
 assert.doesNotThrow(function() {assert.ifError(null);});
 assert.doesNotThrow(function() {assert.ifError();});
 
+assert.throws(() => {
+  assert.doesNotThrow(makeBlock(thrower, Error), 'user message');
+}, /Got unwanted exception. user message/,
+   'a.doesNotThrow ignores user message');
+
 // make sure that validating using constructor really works
 threw = false;
 try {