Petty was hurt on a fluke play in Saturday's 41-3 loss to the New England Patriots, with an MRI exam confirming the team's fears. He was injured while trying to tackle cornerback Malcolm Butler on a fumble return. Afterward, Petty said he "felt something pop" in his shoulder.
The plan is for Petty to have surgery on the shoulder, a league source said.
The Jets haven't named a starter for the final game, a home date against the Buffalo Bills. The only two quarterbacks on the roster are Ryan Fitzpatrick and rookie Christian Hackenberg, who has yet to dress for a game.
Coach Todd Bowles was scheduled for media availability on Monday, but it was cancelled due to a doctor visit, the team announced. He was hospitalized Friday night with kidney and gall bladder issues, which almost prevented him from coaching Saturday's game. He's scheduled to meet the media on Tuesday.
Chances are, Fitzpatrick -- a pending free agent -- will get the start in what probably will be his final game with the Jets.
Bowles said recently he would play Hackenberg onlyin an emergency situation. The Jets drafted him in the second round, but they consider him a major project and want to develop him slowly, although it's possible he could be used off the bench on Sunday.
Petty was supposed to start the final four games in what was considered an audition. The Jets don't have a clear-cut starter for 2017, and they were hoping to form an evaluation of Petty.
He started the last three games (and four overall), finishing with a 1-3 record. He completed only 56 percent of his passes (75-for-133), with three touchdowns and seven interceptions. His passer rating was 60.0.
Petty became the 16th Jets player placed on injured reserve in 2016. To fill his roster spot, they claimed linebacker Corey Lemonier on waivers from the Detroit Lions.