Savage has since cleared the concussion protocol, and he came back in the game for the last 23 seconds of the first half to take a knee.
Savage was initially evaluated on the sideline and was taken to the locker room in the second quarter. On the previous play, Savage ran a successful quarterback sneak on fourth-and-1.
Savage replaced Osweiler in the Texans' Week 15 victory over the Jacksonville Jaguars after Osweiler threw two first-half interceptions. Savage was making just his second career NFL start on Sunday.
The Texans signed Osweiler to a four-year, $72 million contract during the offseason, but he struggled this season, entering the game with 14 touchdowns and 16 interceptions in 14 games this season.
Savage was 5-of-8 for 25 yards and a fumble before he left the game.