The Lakers said Bryant has an avulsion fracture, in which a tiny fragment of bone tears away near a tendon or ligament.
Bryant hurt the top joint on the index finger on his right hand while reaching for a pass along with Minnesota's Ryan Gomes late in the first quarter of the Lakers' game against the Timberwolves.
After getting tape on the finger from trainer Gary Vitti, he returned to the game briefly in the second quarter before going to the locker room for the rest of the half.
Bryant returned after halftime with the finger fully covered in tape, hitting a 3-pointer and two more baskets in the opening minutes.
Bryant is the NBA's second-leading scorer with 28.8 points per game.