Engram was hurt late in the first half of the Giants' 22-16 victory when he was sandwiched by a pair of Jets defenders following a short completion.
The second-year tight end stayed on the field for a while but eventually walked to the sideline without assistance and went directly to the locker room. He had three catches for 23 yards before the injury.
The Giants also lost backup tight end Rhett Ellison to injury in the contest, but Ellison told the New York Daily News that he was poked in the eye.
Engram is expected to be an integral part of the team's offense this season. He led all rookie tight ends with 64 receptions, six touchdowns and 722 receiving yards in 2017.
A first-round pick (No. 23 overall) in the 2017 NFL Draft, Engram had at least four receptions in 11 of his 15 games last season.
In four seasons at Mississippi, the 6-foot-3, 240-pound Engram had 162 catches and 15 touchdowns in 41 games, setting career bests with 65 receptions and eight scores as a senior.
Engram likely would not have played in the preseason finale and now has more than two weeks to prepare for the regular-season opener against the Jacksonville Jaguars on Sept. 9.