Smith was taken out of the game after his touchdown toss with a head injury, which was later ruled to be a concussion.
According to San Francisco head coach Jim Harbaugh, Smith began experiencing blurred vision six plays before his 14-yard touchdown throw to Michael Crabtree after he was hit by St. Louis Rams linebacker Jo-Lonn Dunbar.
Smith was replaced in the game by Colin Kaepernick after his touchdown pass cut the Rams' lead to 14-7, with 8:13 remaining in the second quarter.
Smith was 7-of-8 passing for 72 yards and one touchdown in the game. Kaepernick was 11-of-17 for 117 yards in place of Smith.
Harbaugh said Smith felt better overnight and is expected to see a neurologist on Monday. Smith's status for next Monday's game versus the Chicago Bears is uncertain.