It's an archaic form for the negative mood, mostly used idiomatically now, I guess. It means the same as "don't forget me". " as said by Henry VIII.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
I don't believe I've ever heard anybody use "Forget me not" as a sentence -- only the flower "forget-me-not", shown below.
CJ