On March 10, 2014, during a game against the Columbus Blue Jackets, he collapsed on the team bench. He has had heart conditions in the past and missed a few games the week earlier when he didn't feel well after a game. He is in stable condition. The NHL released a state on Peverley's health saying: "Dallas player Rich Peverley is doing well and is in stable condition. He was transported to the hospital." As a result of the emotional state of the players on both teams caused by the medical emergency, the game was rescheduled to April 9.