Pryor has a tear in his groin and is expected to miss about two weeks.
The Jets are interested in bringing Pryor back when he is healthy, a source told ESPN's Adam Schefter, but other teams also are likely to be interested.
Pryor had only 20 receptions for 240 yards and one touchdown in nine games for the Washington Redskins in 2017.
He signed a one-year, $4.5 million deal, which included a $1 million signing bonus, with the Jets in March.
On Thursday, Pryor expressed confidence in his ability to contribute.
"If I play this week -- hopefully, I do -- I'll come back and dominate and do what I gotta do," Pryor told ESPN. "... I'm a playmaker. Throw me the ball and I'll make it happen."
Pryor has battled injuries since signing with the Jets. In the spring, he fractured an ankle and required surgery, which cost him most of the preseason. The Jets never disclosed the injury. Pryor revealed the nature of the injury in August, resulting in a stern rebuke from coach Todd Bowles.
The wide receiver corps is banged up, and the Jets need bodies. The only healthy receivers are Robby Anderson, Jermaine Kearse, Andre Roberts and Charone Peake. Roberts and Peake are mainly special-teams players.
ESPN's Rich Cimini contributed to this report.