The Chiefs also lost running back Spencer Ware to a concussion during the game against the Colts in Indianapolis.
Colts cornerback Vontae Davis suffered a concussion as well during the game.
Smith first went out of the game in the opening quarter to be evaluated for a concussion after a hard hit but returned in the second quarter after he was cleared.
Then, in the third quarter, Smith hit his head on the turf after being shoved out of bounds on a scramble by Colts defensive back Clayton Geathers and left for good with a concussion.
Nick Foles, who was signed by Kansas City after being released by the Los Angeles Rams in the preseason, replaced Smith.
Smith completed 9 of 19 passes for 127 yards and one touchdown. He also had two carries for 9 yards.
Ware did not return for the second half and finished with 19 yards on seven carries in the first two quarters.