McCown, 38, received a second opinion Monday, with additional tests confirming that he will need surgery -- what the Jets had feared on Sunday night in Denver.
"It's big for him and it's big for us because he's been leading us all year, offensively," said Jets coach Todd Bowles, explaining the impact of the injury. "For him to go down this late in the season ... it's the next-man-up mentality. The next guy has to step up."
Christian Hackenberg, the former second-round pick who has yet to play in nearly two seasons, will be the No. 2 quarterback.
McCown was injured late in the third quarter of the Jets' 23-0 loss to the Broncos. He was tackled by Shane Ray as he released a pass, later saying the Denver pass-rusher "bent it funny" -- meaning his hand -- as they fell to the turf.
"I knew when it happened something wasn't right," McCown said in an emotional news conference after the game.
Beset by injuries in recent years, the well-traveled McCown surprised many by playing every offensive snap in the first 12 games, establishing himself as the leader of the team.
McCown, playing for his eighth team in 15 years, finished with 267 completions, 2,926 passing yards and 18 touchdown passes -- all career highs. He tied a career high with 13 starts, something he hadn't done since 2004.
Bowles said he's had two post-injury conversations with McCown, but they didn't discuss his future with the team. McCown will be a free agent after the season and he hasn't said whether he will try to play next season. The Jets have major decisions to make at the quarterback position, and that could include drafting one in the first round.
Petty, a fourth-round pick in 2015, will make his fifth career start Sunday. He started four games last season but wasn't able to finish the last two because of injuries. In a Christmas Eve loss to the New England Patriots, he suffered a season-ending injury to his left (non-throwing) shoulder on a fluke play in which he tried to tackle a defender on a fumble return.
"He's been taking notes on the sideline," Bowles said of Petty. "He understands what's going to come, but it's an opportunity for him. He'll get the majority of the reps this week and he'll be well-prepared to play in a game on Sunday."