Cumberland suffered the injury during the second quarter of the Jets' 34-24 loss in Oakland on Sunday.
The second-year pro, who had started to gain an expanded role, had two catches for 35 yards this season.
The Jets elevated Jeff Baker from the practice squad to replace Cumberland, according to the Newark Star-Ledger.
Mike Mazzeo is a regular contributor to ESPNNewYork.com. Information from ESPNNewYork.com's Ian Begley was used in this report.