Jackson, one of the team's defensive leaders, was hurt in the second quarter, when the Browns allowed 20 points in a 41-27 loss.
The Browns also lost starting cornerback Dimitri Patterson in the second half to an ankle injury and defensive tackle Ahtyba Rubin to a lower leg injury.
They were without their best cornerback, Joe Haden, who is serving the final game of a four-game suspension.
Giants tight end Martellus Bennett returned in the second quarter after suffering a left knee injury. Bennett was hurt in the first quarter, but was back on the field midway through the second period. He had been injured while blocking on a running play.
Giants backup running back Andre Brown did not return from a head injury after taking a hard hit on a kickoff runback.