Netflix has announced it's plans to support 4k streaming via browser. However, users must meet some pretty strict requirements to achieve the mega-res content.
In order to stream at full 4k resolution, you will need a CPU that can handle 10-bit HEVC codec. Kaby Lake Intel processors now support it, which are really just now hitting computers. The new MacBook and Surface Book, however, do not utilize these processors, so you will be needing a computer from a different manufacturer entirely (Dell, Asus, HP, etc). It also basically requires Windows 10 as you will need Edge as well. Edge is the only browser to support the codec that the industry requires for 4k streaming.
This feature is slated to release this week, granted you meet all the requirements...or you can just watch on a set top box, console, or smart TV like everyone else.