With Rudolph sidelined, the Steelers will stick with Devlin Hodges as the starter as they try to make the playoffs.
Paxton Lynch will be Hodges' backup.
Lynch, a former Broncos first-round pick, was signed to the team's practice squad in September before being elevated to the 53-man roster in October. He's been active for one game, against the Los Angeles Chargers when Rudolph was sidelined with a concussion.
"Week in and week out, even though there were weeks I didn't know if I was going to play or not, I've been preparing like I was going to play," Lynch said. "I know there was a week in Los Angeles that I got bumped up and was one play away from playing. That has been my mindset since I got here: Prepare and get up to speed as fast as I could if my number is called."
Meanwhile, running back James Conner, who left Sunday's game with a thigh injury, told reporters he had an MRI on the injured quad on Monday. He's awaiting results, and his status for Sunday's game hasn't been determined.
"I got an MRI on it," he said. "I got to wait and see what happened officially, but something didn't feel right on it. So I've got to wait and see what they say."
The Steelers benched Hodges on Sunday against the New York Jets after he threw two interceptions in the first half, and put Rudolph into the game. Rudolph threw a touchdown pass near the end of the first half to tie the score but was injured on a hit in the second half, forcing Hodges back into the game, which the Steelers lost 16-10.
Rudolph wasn't available for interviews postgame, but he appeared to be in severe pain as he struggled to get dressed in the locker room afterward. He was spotted with his left arm in a sling as he left the stadium.
The loss took the Steelers' playoff hopes out of their control and put the Tennessee Titans into the final AFC playoff spot heading into Week 17. Tennessee will clinch the final spot if it defeats the Houston Texans.
For the Steelers to make the playoffs, they must win at Baltimore and need the Titans to lose at Houston. The Steelers also could reach the playoffs with a loss but would need help from several teams.
Conner said he was injured on his final carry, which went for a 1-yard loss in the second quarter. Conner took the handoff from Hodges and was promptly brought down by three defenders. He was tackled a little awkwardly as all three collapsed on him, and he knew shortly after that something was wrong.
After winning his first three starts, Hodges has struggled in his past two starts, throwing six interceptions in the two losses. The undrafted rookie has completed 67.4% of his passes but has thrown eight interceptions and just five touchdown passes in his five starts.
"I don't think I'm a bad player," Hodges said Sunday. "I've just been playing bad."
Rudolph, in his second season, has completed 62.2% of his passes in 10 games this season, for 1,765 yards with 13 touchdown passes and nine interceptions.
ESPN's Brooke Pryor contributed to this report.