Cunningham injured his Achilles tendon during Saturday's practice, and the linebacker will require surgery and be out for the season, according to Jets coach Rex Ryan.
"That's obviously bad news there for us. The young man was really coming on. We're certainly going to miss him," said Ryan.
Cunningham played two games for New York last season after being released by San Francisco.
Campbell, a former fourth-round pick in 2010, signed with the Redskins in March but had his deal voided after he failed a physical. He was invited as a tryout player to the Jets' full-squad minicamp in June.
- Molly Geary