Murray broke the fourth metacarpal in his left hand during the fourth quarter of last Sunday's win over the Eagles and underwent surgery on Monday.
On Wednesday, head coach Jason Garrett said Dallas needs to know whether Murray has the ability to carry the ball to determine if he can play. Murray wore a cast on his left arm at practice and was allowed to catch a few passes during individual drills, according to USA Today.
Murray has rushed for 1,687 yards this season and leads the NFL in carries and rushing touchdowns.
The Cowboys (10-4) host Indianapolis (10-4) on Sunday.
- Molly Geary