The Predators announced the suspensions Tuesday morning and did not specify which rules the forwards broke.
General manager David Poile says in a statement that the Predators have a few simple rules and violating them is "not fair" to the club and their teammates.
Radulov was criticized for his performance in Sunday night's 5-3 loss at Phoenix, which dropped the Predators into an 0-2 deficit in this Western Conference semifinal. Radulov rejoined Nashville in March after spending the past four years in Russia. He has six points.
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