Per Robert Littal of Black Sports Online, Savage's hands shook after he absorbed a big hit in the second quarter, and he returned to the game briefly before exiting again.
Savage was replaced by veteran T.J. Yates.
Savage, 27, won the team's starting job early in the offseason, though he kept it for all of one half after losing two fumbles and watching the Jacksonville Jaguars march out to a 19-0 lead. Deshaun Watson took over and was a revelation before tearing his ACL during practice in early November.
This season, Savage has thrown for 1,412 yards, five touchdowns and six interceptions.
With Savage sidelined, Yates now steps into the spotlight for Houston. The career backup has appeared in 19 games and entered Sunday's contest with 1,534 yards, six touchdowns and eight interceptions during his NFL tenure.
The Texans could also seek to upgrade the position in free agency while Savage is sidelined. Colin Kaepernick, for instance, would be an excellent fit for the zone-read attack the Texans utilized while Watson was healthy.
Regardless of how the Texans handle the Savage injury, quarterback went from being one of the team's strong points under Watson to a major weakness.