Nashville general manager David Poile announced the decision Tuesday in a statement but did not elaborate on what rules were broken. The Predators trail the Coyotes 2-0 ahead of Wednesday's critical Game 3 in Nashville.
Radulov returned to the Predators in March after bolting to the Russian KHL following the 2007-08 season. He had three goals and four assists in nine regular-season games. The 25-year-old has one goal and five assists in five playoff games.
The Predators acquired Kostitsyn from the Montreal Canadiens prior to the trade deadline in hopes of bolstering their attack for the post-season.
The 27-year-old had four goals and eight assists in 19 games with the Preds, after collecting 24 points (12-12) with the Habs.
Kostitsyn has three goals and an assist so far in this year's playoffs.
"The Nashville Predators have a few simple rules centred around doing the right things," Poile said. "We have always operated with a team-first mentality and philosophy. Violating team rules is not fair to our team and their teammates."
Nashville defeated the Detroit Red Wings in fives games in the first round of the playoffs.