Is it possible to gain muscle mass and do karate at the same time?

Yes: Add some weight training to your workouts, this will help.

Yes, but....: you might not want to gain too much muscle mass unless you are really on the thin side. Karate is a sport that relies on quickness, fast reflexes and flexibility. Gaining too much muscle mass can sometimes get in the way of that. A little muscle mass is okay, but don't overdo it! If you look at most the UFC champions they are not huge guys that you would see on the cover of a muscle magazine!