He suffered the injury in Week 5 against the Seattle Seahawks and was out for most of the second half.
Cook's absence is a prime opportunity for Alexander Mattison and Mike Boone to earn more carries.
Through Week 5, Mattison has 219 rushing yards and a touchdown, while Boone has 19 rushing yards on two attempts, both taking place after Cook's injury last week.
Last year, the Vikings drafted Mattison No. 102 overall out of Boise State. Boone, who played his college football at Cincinnati, is in his third season.
ESPN ranked the 22-year-old Mattison as the No. 46 running back in PPR leagues before the season—Boone, 25, was not listed in the top 70—and the Vikings believed he could be an X-factor for the club.
"When he went in there last year, he did a nice job," Minnesota head coach Mike Zimmer told reporters during training camp. "I was very impressed with him. I think he's going to be a very good back. Dalvin has helped him quite a bit, and so has [Vikings running backs coach] Kennedy Polamalu."
There's one name on the Vikings depth chart that will stand out to longtime fantasy players but should probably be avoided: Ameer Abdullah.
The former Detroit Lion is fourth on the Vikes' depth chart and isn't likely to see many touches despite his experience. Andrew Krammer of the Minneapolis Star-Tribune noted prior to the season that Abdullah would be used mostly on third downs and in the return game. He doesn't have a carry this year.