Murray suffered the injury in the first quarter of Sunday's 37-34 loss to the New York Giants, forcing the rookie running back to end his season with 897 rushing yards.
With Murray out, the Cowboys will need to find a running back. Or two.
Veteran Sammy Morris is scheduled to visit Valley Ranch on Tuesday and is expected to sign with the Cowboys, owner Jerry Jones said on his radio show.
In 11 seasons with Buffalo, Miami and New England, Morris has 2,955 rushing yards and 26 touchdowns on 708 carries. He was cut by the Patriots after training camp this year.
Morris played with Jason Garrett in Miami in 2004 and was on the Dolphins in 2005-06 when Garrett was the quarterbacks coach, so he would have some familiarity with the offense.
Morris had 56 yards on 20 carries last year in New England and only 17 yards on seven caries in the preseason before his release.
Another possibility is Lonyae Miller. He was among the Cowboys' final training camp cuts and is currently on Oakland's practice squad. He played in four games last year but did not record a carry, playing solely on special teams. He had 37 yards on 23 preseason carries to go with four catches for 15 yards.
Todd Archer covers the Cowboys for ESPNDallas.com.