Adrian Peterson will most likely miss next week, possibly the rest of the season
It would be a bit foolish to risk further injury to Peterson, their franchise player, when there's nothing on the line except draft position. That's the situation the Vikings are facing right now, sitting at 3-9-1 and in last place in the NFC North.
The Vikings are currently in line to get the 4th pick in the NFL Draft, and to be honest, they might be better off sitting Peterson even if he's healthy, just to get the best possible pick. They're only a half a game ahead of Atlanta and Washington, and a game and a half ahead of Houston, who is currently in line for the top overall pick.