Per Rapoport, Darnold will attempt to manage and work through the injury.
Earlier in the day, Jets head coach Adam Gase discussed the situation.
"We want to make sure we're not putting him in harm's way where any further damage can be done," Gase added.
The third-year signal-caller missed time after suffering a shoulder sprain during a Week 4 loss to the Denver Broncos. Veteran quarterback Joe Flacco made his first start in almost a year in Week 5's 30-10 loss against the Arizona Cardinals, with Darnold "in a lot of pain," according to Gase (h/t ESPN).
He returned in Week 7 but has struggled over the last two games with no touchdowns and two interceptions.
The Jets haven't been better without him, going 0-8 in games that Darnold has not started since the 23-year-old joined the team as the third overall draft pick in 2018.
Before he was sidelined for Week 5, the USC product was 82-of-138 passing for 792 yards, three touchdowns and as many interceptions to follow up on a sophomore campaign in which he threw for 3,024 yards and 19 touchdowns through 13 games. He missed time last season after he contracted mononucleosis and suffered an enlarged spleen as a complication.
He started 13 games as a rookie, going 4-9 with 2,865 yards, 17 scores and 15 interceptions.
Flacco was inactive for Jets' first three games in 2020 and played four snaps in Week 4, going 2-of-2 passing against his former team. Fourth-round rookie James Morgan is listed as the third-string QB.