General Manager David Poile said the move was due to an unspecified violation of team rules.
"The Nashville Predators have a few simple rules centered around doing the right things," Poile said in a statement. "We have always operated with a team-first mentality and philosophy. Violating team rules is not fair to our team and their teammates."
The absence of Radulov and Kostitsyn will be a key factor the third contest of the Preds' best-of-seven series against the Phoenix Coyotes, which Nashville trails 2-0.
Radulov is the team's leading post-season scorer with six points in seven games. Kostitsyn is tied for the team lead with three goals.