He was officially ruled out not long after the noncontact injury on a pass rush in the first quarter.
Carter had 14 tackles and one sack entering Sunday's game in Arlington, Texas. He led the Giants with nine quarterback pressures the first four weeks, according to Next Gen Stats.
Carter, 24, has been playing 89% of the defensive snaps for the Giants. His absence, especially long term, would leave the Giants shorthanded on the edges; outside linebacker Oshane Ximines was placed on injured reserve earlier this week with a shoulder injury.