On March 1, 2010, the Oilers traded Grebeshkov to the Nashville Predators in exchange for a second-round draft pick in 2010. On March 2, he scored a goal in his Predators debut in a 4–3 win, ironically coming against the Oilers. In just his fourth game with the Predators, Grebeshkov took a shot in the groin against the Vancouver Canucks. Though he continued to play following the blocked shot, he required emergency surgery on one of his testicles following the game, causing him to miss the remainder of the regular season. Grebeshkov was cleared to play prior to Game 2 of the Predators' Western Conference Quarter-final match-up against the Chicago Blackhawks. However, he was a healthy scratch for Games 2, 3 and 4 as Predators Head Coach Barry Trotz elected to play rookie Cody Franson in his place. Grebeshkov made his Stanley Cup playoff debut in Game 5, registering two assists in the 5–4 Predators loss.