Cook, the Seminoles' star running back, injured his shoulder after being pinned in a pass-protection drill, and coach Jimbo Fisher said Cook underwent surgery Tuesday.
Cook is not in jeopardy of missing preseason camp, which usually begins the first week of August.
"We cleaned up a little stuff in the back of the shoulder," Fisher said. "He'll be ready to go June, July and train and do everything. We had him checked, and it was questionable whether to do it or not, so they went ahead, and good thing they did. It's nothing drastic."
As a sophomore last season, Cook rushed for 1,691 yards and 19 touchdowns. After receiving seven first-place votes for the 2015 Heisman Trophy, he was considered one of the favorites to win the prestigious award this coming season.
Cook missed all of spring practice in 2014 as a true freshman after injuring the labrum in his right shoulder, but Fisher said the latest injury is not related to that one. Cook also had left shoulder surgery before enrolling at Florida State.
Florida State is limited at running back for Saturday's spring game, with Mario Pender and Johnathan Vickers also out with injuries this spring. Jacques Patrick and Ryan Green are the remaining scholarship running backs. Fullback Freddie Stevenson figures to also receive carries in the spring game.
Fisher praised Patrick, who is 6-foot-2, 233 pounds, as well as Green following a weekend scrimmage.
"Jacques you saw him flash and make some plays," Fisher said Saturday. "He took some runs that I wanted to see him do -- 3- or 4-yard runs he made 6- or 7-yard runs. He started running with the power and size he has and pushing the pile.
"Ryan Green, saw him flash at times."
Fisher added Wednesday that quarterback Sean Maguire is on pace to begin working out again this summer. Maguire's left foot remains in a boot after undergoing surgery for a fractured ankle in early January. A senior, he has not practiced this spring, but he was throwing passes after practice with the boot on Wednesday.