Cats can get acne just like teenagers. Unlike teens, feline acne can be a life-long problem. Daily soaks with Epson salts or applying antibacterial and/or antifungal creams on the chin help disinfect the area. Some cats require long-term antibiotics and some even benefit from human acne medications. (Don't apply any medication without your veterinarian's recommendation.) The cause of feline acne has not been determined and without proper veterinary care, can progress to serious skin infections.
For more information, please read the article Acne in Cats.