Martinez is coming off a torn anterior cruciate ligament that ended his 2021 season after only three games. He took a pay cut this offseason to return to the Giants.
Martinez sat out the first preseason game but played eight snaps in the second preseason game and 18 last week.
He spent the past two seasons with the Giants after four seasons with the Packers, who drafted him in the fourth round in 2016. Martinez has totaled 686 tackles, 13 sacks, four forced fumbles, four interceptions and 22 pass breakups in 80 career games.
The Giants also cut veteran tight end Rick Seals-Jones from injured reserve with an injury settlement. A toe injury landed Seals-Jones on injured reserve.