Cook missed practice this week because of a hamstring injury he sustained last week against the Green Bay Packers. Cook said it was only a cramp, but the Vikings aren't taking any chances after he missed all but four games in 2017 because of an ACL tear.
In two games, Cook had a total of 78 yards rushing on 26 carries without a touchdown.
With Cook on the sidelines, Latavius Murray will get the start at running back against a Buffalo defense that ranks 22nd in the NFL after two weeks.
Backup running back Mike Boone also could see playing time for the first time during the regular season after playing well during the preseason.
Griffen played against the Packers despite a toe injury, but missed practice on Wednesday because of a knee injury he suffered against Green Bay. He had six total tackles and was credited with two half-sacks in the first two games.
Zimmer also said center Pat Elflein will play for the first time this season against the Bills after missing the first two games because of shoulder and ankle injuries. He was a full participant in practice beginning Wednesday.