"Not the way any of us wanted it to go, but we know the commitment you've made to this team will continue to impact us moving forward," the Jets said in a statement Tuesday.
Hope, hype and anticipation evaporated within minutes when Rodgers went down shortly after making his debut against the Buffalo Bills on Monday night.
During a postgame press conference, Jets' head coach Robert Saleh said they had feared that Rodgers suffered a torn Achilles, saying "it's not good."
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"Personally, I don't hurt for me, I don't hurt for our locker room. I hurt for Aaron and how much he's invested in all of this," Saleh said.
The star quarterback was sacked by Buffalo's Leonard Floyd on the fourth snap of the season.
The 39-year-old tried to spin out of Floyd's grasp. In doing so, he appeared to twist his left ankle. He stayed down and the Jets' medical personnel rushed immediately to him.
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Rodgers spent a few minutes in the injury tent before being loaded onto a cart. He got out of the cart before leaving the field and limped to the locker room through the tunnel at midfield.
The Jets announced it as an ankle injury, saying his return was questionable before later ruling him out for the rest of the game.
Rodgers was seen entering the X-ray room with his left foot in a boot. According to the Jets, X-rays on the ankle were negative.
In a sideline interview with ESPN's Lisa Salters, Jets coach Robert Saleh said only that Rodgers was getting checked out and "we'll know more later."
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Rodgers was replaced in the game by Zach Wilson, who took over backup duties when the Jets traded for Rodgers in the offseason.
Wilson, drafted second overall in 2021, was demoted twice last season.
The Jets were able to pull off a dramatic 22-16 overtime victory thanks to a 65-yard punt return touchdown from Xavier Gipson, but that celebration may be short lived depending on Rodgers' injury update on Tuesday.
Rodgers' injury Monday night was reminiscent of the 1999 opener, when starter Vinny Testaverde suffered a season-ending Achilles injury in the second quarter.
ESPN contributed to this report.