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.