I'm not a doctor, but I play on on the Internet. In response to the OP, a lot depends on which tendon in which finger needs repaired and what you do with that finger. Almost always, a repaired tendon will be shorter than it was.
My cousin's kid (a violin player) recently severed a tendon in the ring finger of his right hand. It should heal nicely, and give his finger a permanent curve. He'll still be able to play the violin, but it would have been worse if it had been any other finger on either hand.
Steve