Cook broke his right arm Thursday night against Tampa Bay and he will need seven or eight weeks to recover from surgery.
"He's distraught. It's tough. It's tough," coach Leslie Frazier said.
The NFL's new rule this year allows each team the opportunity to keep one player on revocable injured reserve, so Cook could return for the Dec. 30 season finale against Green Bay or the playoffs if the Vikings (5-3) can survive a difficult second half of their schedule and qualify. The designated player is required to miss at least six weeks of practice and be inactive for at least eight weeks.
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The Vikings didn't immediately make a move to fill Cook's roster spot, but Frazier said they might hold some workouts with candidates this weekend. The Vikings have nine days before their next game at Seattle.
Rookie Josh Robinson will take Cook's place in the starting lineup. A.J. Jefferson, acquired in a trade with the Arizona Cardinals right before the season, will probably become the nickel cornerback. Marcus Sherels and Brandon Burton are the other cornerbacks currently on the roster.
Cook was hurt helping make a tackle of running back Doug Martin early in the third quarter. Martin scored on a 64-yard pass on the next play, and the Buccaneers completed four third-and-long passes during their game-sealing touchdown drive midway through the fourth quarter. Frazier declined to speculate about whether Cook's absence directly led to that score.
"Everybody has injuries in our league, and we're going to play games in the future now without him. So someone else will have to step up and make those plays for us," Frazier said.
Cook, in his third year out of Virginia, has been the team's best player in man-to-man coverage. He helped limit three star wide receivers to minimal production in games this year. Detroit's Calvin Johnson was targeted 12 times and had just five catches for 54 yards on Sept. 30. Arizona's Larry Fitzgerald caught four passes for 29 yards after having seven passes thrown his way last Sunday. Vincent Jackson had only two receptions for 40 yards on six targets Thursday.
"I thought he was really coming along, and he had a good game yesterday in the time that he was out there," Frazier said. "He was playing well for us, so it's unfortunate."
Cook's rookie season was limited to six games because of torn meniscus cartilage in both of his knees that resulted in lingering post-surgical inflammation. Last year, he played in only six games, too, missing the remainder of the season after being jailed on felony assault charges the day before the Vikings played Green Bay.
Cook was kept on the roster but away from the team until his acquittal by a jury in March.