Durant sustained a torn biceps during Monday's loss to the Washington Redskins. The 29-year-old was Dallas' leading tackler through eight games with 49, and also had four pass defenses, an interception and two forced fumbles.
The Cowboys also announced that they signed veteran linebacker Tim Dobbins.
Dobbins was drafted by the San Diego Chargers in the fifth round in 2006 and has appeared in 110 career games, making 22 starts. The 31-year-old appeared in three games for the Houston Texans in 2013, but he has not made an NFL start since the 2012 season.
- Brad Rowland