Murray suffered the injury in the first quarter of Sunday night's game against the New York Giants.
The injury puts an end to Murray's impressive rookie season, in which he set a franchise record with 253 yards rushing in a Week 7 win over St. Louis. Since then he has started every game since for the Cowboys.
Murray amassed 897 yards and two touchdowns on 164 carries, while adding 26 receptions for 183 yards.
Cowboys safety Barry Church was also injured in Sunday's game and was placed on injured reserve with a shoulder injury.
Church has played in all 13 games for Dallas this season, recording 28 tackles.
To fill the roster spots, Dallas signed running back Sammy Morris and safety Mana Silva to the active roster, and also signed cornerback C.J. Wilson to the practice squad.