Hmmm...what kind of fish? Did you just get the tank and add fish, or "cycle" the tank? (Lot of ways to do this cycling thing; if you send a message to one of the resident experts, like Roan Art, you'll get great answers).
They may be nipping each others fins, my black skirt tetras do that to each other all the time. As long as the rips are tiny (not so much missing that the fish can no longer swim properly), and they don't get fuzzy white stuff on them or anything abnormal, all should be fine. If the fish are healthy and eating quality food they should heal quickly.