Smith rolled his ankle during the fourth play of the Jets' opening drive in the second half of their 26-17 loss to the Detroit Lions on Thursday. Smith returned to the game after having his ankle taped, but walked to the locker room later in the quarter to have the injury examined.
X-rays were negative, and Smith told reporters after the game that the ankle was "just a little sore."
Smith is competing for the Jets' starting job with Mark Sanchez, who has thrown one more interception than touchdown pass in his career after a 13 touchdown, 18 interception performance in 2012.
Sanchez was 10-of-13 for 125 yards, a scoring pass and a pick on Thursday. Smith was 6-of-7 for 47 yards in limited action.