I doubt the algae will hurt your snake, but I'd be concerned that if the algae can grow, what else might be growing that you can't see?

First thing I would do is make sure you have killed the algae. Just washing it until you can't see it won't kill all of it. You will need to use bleach or something else that will kill it.

Once you have killed it off, I bet it won't come back nearly as quickly. To make sure it stays gone, change the water more often and clean it thoroughly each time.