Thompson was hurt with 10:40 left in the fourth quarter of Golden State's 109-104 victory. He left the game nearly three minutes later before going to the locker room.
"Klay said he'll be fine, but Klay can be half-dead and he'd say he would be fine," Kerr said.
Thompson told reporters he was confident he wouldn't miss any time.
Thompson had a team-high 25 points, five rebounds and five assists in 32 minutes Sunday night. The three-time NBA champion made four of his six three-point shots.
Game 3 of the NBA Finals is Wednesday night at Oracle Arena in Oakland, Calif.