Rodgers, 39, was replaced by former No. 2 overall pick Zach Wilson. The four-time NFL MVP was carted off the field and brought into the Jets' locker room.
Monday Night Football play-by-play man Joe Buck said Rodgers was reported to have suffered an ankle injury and his status is "questionable."
In May, the Athletic's Dianna Russini, then working for ESPN, reported that Rodgers appeared to suffer a potential injury during the Jets' OTAs session and was seen "favoring his ankle.
The Jets acquired Rodgers in a blockbuster trade with the Green Bay Packers, with whom the quarterback spent the entirety of his 18-year NFL career, last month.
Rodgers had previously announced his intention to play for the Jets during an appearance on the Pat McAfee Show prior to the completion of a deal. Rodgers met with Jets owner Woody Johnson and a contingent of team representatives in California on March 7. New York had previously acquired Rodgers' predecessor, Brett Favre, in a trade with the Packers in 2008, which led to the eventual four-time NFL MVP taking over as Green Bay's starting quarterback for the remainder of his tenure with the franchise.
In January, ESPN's Adam Schefter reported that the Jets were "a very real scenario" in a possible trade for Rodgers even prior to the recent hiring of Nathaniel Hackett as offensive coordinator, who had previously held the same position in Green Bay and Rodgers had publicly praised following his hiring as the Denver Broncos' head coach last offseason. Rodgers led the NFL's top scoring offense during the first of two consecutive Associated Press Most Valuable Player award-winning seasons in 2020, both of which took place during Hackett's tenure with the Packers.
Rodgers leads all Packers quarterbacks with 475 touchdowns and ranks second in franchise history behind only Favre in QB wins (147), completions (5,001) and passing yards (7,660).