Luck showed symptoms of a concussion on Monday after taking a sack in the fourth quarter of Sunday's game against the Tennessee Titans when his head bounced off the turf. He did not practice all week as the Colts prepared for the Thanksgiving game.
Luck must clear the NFL's concussion protocol before he is allowed to play.
After the Steelers game, the Colts will travel to play the New York Jets on Dec. 5 in a "Monday Night Football" game. Luck will miss his 10th game since Week 4 of last season.
Tolzien is 56-of-91 passing for 721 yards, a touchdown and five interceptions in six career appearances.
The Colts promoted quarterback Stephen Morris to the 53-man roster from the practice squad to back up Tolzien.
Morris has never played in a regular-season game. He spent the entire season on the Colts' practice squad. He participated in Indianapolis' offseason program and training camp before being waived on Sept. 7 and signed to the practice squad the following day.
Morris was signed to the Colts' 53-man roster off of the Philadelphia Eagles' practice squad on Dec. 24, 2015. He spent most of the 2015 season on the Eagles' practice squad.
In 2014, Morris spent most of his rookie season on the Jacksonville Jaguars' practice squad before being elevated for the last two weeks of the season. Morris originally signed with the Jaguars as an undrafted free agent on May 12, 2014, out of Miami.
Wide receiver Devin Street was waived to make room for Morris. Street played in three games for Indianapolis this season and caught one pass for 20 yards.
The Colts also ruled out starting safety Clayton Geathers (concussion) for Thursday's game.