diff --git a/doc/api/assert.md b/doc/api/assert.md
index b1175e5e489e5d..5f331fdef35604 100644
--- a/doc/api/assert.md
+++ b/doc/api/assert.md
@@ -124,7 +124,7 @@ changes:
 * `expected` {any}
 * `message` {any}
 
-Generally identical to `assert.deepEqual()` with three exceptions:
+Generally identical to `assert.deepEqual()` with a few exceptions:
 
 1. Primitive values are compared using the [Strict Equality Comparison][]
   ( `===` ). Set values and Map keys are compared using the [SameValueZero][]
@@ -132,6 +132,7 @@ Generally identical to `assert.deepEqual()` with three exceptions:
 2. [`[[Prototype]]`][prototype-spec] of objects are compared using
   the [Strict Equality Comparison][] too.
 3. [Type tags][Object.prototype.toString()] of objects should be the same.
+4. [Object wrappers][] are compared both as objects and unwrapped values.
 
 ```js
 const assert = require('assert');
@@ -161,6 +162,11 @@ assert.deepEqual(date, fakeDate);
 assert.deepStrictEqual(date, fakeDate);
 // AssertionError: 2017-03-11T14:25:31.849Z deepStrictEqual Date {}
 // Different type tags
+
+assert.deepStrictEqual(new Number(1), new Number(2));
+// Fails because the wrapped number is unwrapped and compared as well.
+assert.deepStrictEqual(new String('foo'), Object('foo'));
+// OK because the object and the string are identical when unwrapped.
 ```
 
 If the values are not equal, an `AssertionError` is thrown with a `message`
@@ -641,3 +647,4 @@ For more information, see
 [enumerable "own" properties]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Enumerability_and_ownership_of_properties
 [mdn-equality-guide]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Equality_comparisons_and_sameness
 [prototype-spec]: https://tc39.github.io/ecma262/#sec-ordinary-object-internal-methods-and-internal-slots
+[Object wrappers]: https://developer.mozilla.org/en-US/docs/Glossary/Primitive#Primitive_wrapper_objects_in_JavaScript
diff --git a/lib/assert.js b/lib/assert.js
index 73c4a1c444e2df..21c93e96b2a657 100644
--- a/lib/assert.js
+++ b/lib/assert.js
@@ -202,13 +202,30 @@ function strictDeepEqual(actual, expected) {
     if (!areSimilarTypedArrays(actual, expected)) {
       return false;
     }
-
     // Buffer.compare returns true, so actual.length === expected.length
     // if they both only contain numeric keys, we don't need to exam further
     if (Object.keys(actual).length === actual.length &&
         Object.keys(expected).length === expected.length) {
       return true;
     }
+  } else if (typeof actual.valueOf === 'function') {
+    const actualValue = actual.valueOf();
+    // Note: Boxed string keys are going to be compared again by Object.keys
+    if (actualValue !== actual) {
+      if (!innerDeepEqual(actualValue, expected.valueOf(), true))
+        return false;
+      // Fast path for boxed primitives
+      var lengthActual = 0;
+      var lengthExpected = 0;
+      if (typeof actualValue === 'string') {
+        lengthActual = actual.length;
+        lengthExpected = expected.length;
+      }
+      if (Object.keys(actual).length === lengthActual &&
+        Object.keys(expected).length === lengthExpected) {
+        return true;
+      }
+    }
   }
 }
 
diff --git a/test/addons-napi/test_conversions/test.js b/test/addons-napi/test_conversions/test.js
index 73d2c3314f600b..aebf13ba0217ae 100644
--- a/test/addons-napi/test_conversions/test.js
+++ b/test/addons-napi/test_conversions/test.js
@@ -103,7 +103,6 @@ assert.strictEqual(0, test.toNumber([]));
 assert.strictEqual(0, test.toNumber(false));
 assert.strictEqual(0, test.toNumber(null));
 assert.strictEqual(0, test.toNumber(''));
-assert.ok(Number.isNaN(test.toNumber(Number.NaN)));
 assert.ok(Number.isNaN(test.toNumber({})));
 assert.ok(Number.isNaN(test.toNumber(undefined)));
 assert.throws(() => test.toNumber(testSym), TypeError);
@@ -116,7 +115,6 @@ assert.deepStrictEqual(new Boolean(false), test.toObject(false));
 assert.deepStrictEqual(new Boolean(true), test.toObject(true));
 assert.deepStrictEqual(new String(''), test.toObject(''));
 assert.deepStrictEqual(new Number(0), test.toObject(0));
-assert.deepStrictEqual(new Number(Number.NaN), test.toObject(Number.NaN));
 assert.deepStrictEqual(new Object(testSym), test.toObject(testSym));
 assert.notDeepStrictEqual(false, test.toObject(false));
 assert.notDeepStrictEqual(true, test.toObject(true));
diff --git a/test/parallel/test-assert-deep.js b/test/parallel/test-assert-deep.js
index d075f91b5954d0..de6cafdaf86fba 100644
--- a/test/parallel/test-assert-deep.js
+++ b/test/parallel/test-assert-deep.js
@@ -439,4 +439,23 @@ assertOnlyDeepEqual([1, , , 3], [1, , , 3, , , ]);
   assertOnlyDeepEqual(err1, {}, assert.AssertionError);
 }
 
+// Handle boxed primitives
+{
+  const boxedString = new String('test');
+  const boxedSymbol = Object(Symbol());
+  assertOnlyDeepEqual(new Boolean(true), Object(false));
+  assertOnlyDeepEqual(Object(true), new Number(1));
+  assertOnlyDeepEqual(new Number(2), new Number(1));
+  assertOnlyDeepEqual(boxedSymbol, Object(Symbol()));
+  assertOnlyDeepEqual(boxedSymbol, {});
+  assertDeepAndStrictEqual(boxedSymbol, boxedSymbol);
+  assertDeepAndStrictEqual(Object(true), Object(true));
+  assertDeepAndStrictEqual(Object(2), Object(2));
+  assertDeepAndStrictEqual(boxedString, Object('test'));
+  boxedString.slow = true;
+  assertNotDeepOrStrict(boxedString, Object('test'));
+  boxedSymbol.slow = true;
+  assertNotDeepOrStrict(boxedSymbol, {});
+}
+
 /* eslint-enable */