Murray was hurt on a low tackle by Giants defensive end Dave Tollefson with under five minutes remaining in the first quarter.
He remained on the ground for a few moments, then needed help limping to the sideline. His return is uncertain.
Murray, a rookie, set a franchise record with 253 yards rushing in a Week 7 win over St. Louis and has started every game since for the Cowboys.
Felix Jones broke off a 26-yard run three plays after Murray came out of the game, setting up a touchdown.