The New York Daily News reported that Darnold has a "significant sprain" and will miss Sunday's contest versus the Bills (2-7).
Josh McCown, 39, is expected to get the nod for the Jets (3-6) in place of Darnold, who was the third overall pick of the 2018 NFL Draft.
New York will then go into its bye before returning to face the New England Patriots in Week 12.
Darnold was sacked four times and hit on seven occasions in Sunday's 13-6 setback to the Miami Dolphins. He completed 21 of 39 passes for 229 yards and four interceptions.
"Yeah, I feel fine," the 21-year-old Darnold said on Monday. "Some bumps and some bruises but everything is good."
Darnold is 159 for 289 for 1,934 yards with 11 touchdowns and 14 interceptions in nine games this season.
McCown is coming off one of the most productive seasons of his career in 2017. He completed 67.3 percent of his passes and threw a career-high 18 touchdown passes with nine interceptions in 13 games before sustaining a broken left hand.