Smith limped off the field after three BYU tacklers dragged him down in the backfield on a third-quarter rushing attempt. He was later carted off the field and returned to the sideline with a walking boot on his right foot.
A Michigan spokesman said the boot was a precautionary measure, and coach Jim Harbaugh said initial X-rays on Smith's foot were negative.
Smith said he expects to play next week.
Smith ran for 125 yards and a touchdown on 16 carries before leaving the game. He led the charge for a Michigan rushing attack that has racked up more than 200 yards on the ground in each of its last three games.