What to do about a friend who acts childish?

I have a friend at work who likes to be nosey about my personal life with a guy friend. He is my ex but she constantly says hes my boyfriend when he's not. umes that me and this guy are still sleeping together and makes a point of telling other people at work this. When i tell her i dont want it spoken to everyone because we are not in a relationship. She just clammed up and ignored me for the rest of the day! What kind of friend is that? And what if anything can i do about it?