That means veteran quarterback Josh McCown will make his first start of the season on Sunday.
While Jets head coach Todd Bowles announced on Thursday that Darnold would not be the starter, he did not rule out the possibility that Darnold would be active and serve as McCown's backup against the Bills.
If the Jets decide not to have Darnold on the 53-man active roster, they could pull up quarterback Davis Webb from the practice squad.
Darnold played poorly in Sunday's 13-6 loss to the Miami Dolphins, throwing four interceptions with no touchdown passes. He suffered his injury during that game.
For the season, he has more interceptions (14) than scoring passes (11).
The 39-year-old McCown has not attempted a pass this season, but he started 13 games for the Jets last season when he completed 67.3 percent of his passes for 2,926 yards, 18 touchdowns and nine interceptions. The Jets went 5-8 in the games he started a year ago.
The Jets are the eighth NFL team McCown has played for in his 15-year pro career.