Despite starting only seven games this season, Murray rushed for 897 yards on 5.5 yards a carry with 2 TD's, the most for any Cowboys rookie running back since Emmitt Smith.
He will be replaced in the starting line-up by former starter Felix Jones, who had a solid effort against New York last night, rushing for 106 yards on 16 carries, although he did have an extremely costly fumble at the end of the first half that gift-wrapped three points for the Giants.
But, after Jones, Dallas is extremely thin at running back, as they released Tashard Choice earlier in the season and placed rookie Philip Tanner on injured reserve.
Jones has also been extremely injury-prone throughout his four-year career, including missing four games with a high-ankle sprain this season.
The Cowboys are likely to scour the list of available RB's in the next few days to find a backup for Jones, who should receive most of the carries in Murray's absence.