I've looked into this as well and never found something that was exactly what I wanted. Most programs focus on computer science/software programming and have web dev classes available, but don't focus on them.

Why would you want a graduate degree in building web development exactly?

Graduate programs in cs are geared either towards research or higher level subjects. Basic web apps are well basic as far as a subject goes. Its easier to just learn that from a book. Now if you want to learn about databases or security or analytics or something like that. Which tends to be higher level. You should be able to find programs geared around them.

Regardless of whether there are, it would be infinitely more beneficial to buy a few books and jump in on your own.

Theory and practice assignments can only teach you so much. You really need to be creating real applications to understand performance, reliability, and security.