NFL Media's Albert Breer reported Sunday that Lee suffered a strained hamstring, according to a source informed of the injury.
Justin Durant, who replaced Lee in the lineup, also left with a hamstring injury. He also missed the remainder of the game.
Lee had amassed 90 combined tackles and four interceptions heading into the tilt against the Saints. His departure is a costly blow to a Cowboys defense already missing the presence of cornerback Morris Claiborne (hamstring) and defensive tackle Jason Hatcher (neck), who were both declared inactive before the game.
Saints tight end Ben Watson also left Sunday's game, exiting midway through the third quarter with a concussion. Watson leaped in the end zone to catch a Drew Brees pass, hitting his head hard on the turf after losing control of the ball.