File "masturbation causes acne" under acne myths. There is absolutely no truth to this idea whatsoever. Masturbation does not cause acne. Neither does having sex.
This tall tale probably came into being because acne first appears during puberty. This is also the same time of life when sexuality and sexual feelings arise. Although the two may emerge at coinciding times, one is not caused by the other.
Acne really develops from the hormonal changes that occur in the body during puberty. Most teens have at least the occasional breakout; even some adults suffer from acne.
No matter what, try not to feel embarrassed about your skin. You didn't do anything to cause your acne.