It depends on what she's doing to embarrass you. And if it's voluntary or involuntary, like Tourette's. If it's voluntary, like trying to be funny, or being out spoken. Then you'll have to weigh the pros and cons of your friendship and decide. But if it's something that she has no control of, like Tourettes.Then you should stay and keep your friendship. And walk with your head up high.
If you want to keep them as a friend because you like other qualities about them, maybe trying to sit down with them, and tell them you feel she embarrasses you and makes you uncomfortable. If that still doesn't work, then maybe try embarrassing her on some things(not too severe) and try to relate to her what it feels like. Hope it works out for you. =)
It depends on how she is embarassing you. Is she embarassing to hang around? Is she a worthy friend to keep? Tell her she embarasses you. It's not fair to say "I'm not your friend anymore." Like a four year old and not tell her why