In a statement released Tuesday, Stars GM Jim Nill said Peverley is undergoing tests to determine what caused a cardiac incident on Monday night in Dallas.
Peverley, a 31-year-old from Kingston, Ont., underwent a procedure six months ago to correct an irregular heartbeat, and also missed a game last week with a recurrence of the problem.
Monday's game was stopped 6:23 into the first period, when Dallas players noticed their teammate in distress and jumped over the boards to stop the game.
As medical staff rushed to help Peverley, players and staff on both teams were clearly shaken, and a postponement of the game was announced about 30 minutes later.
Dr. Gil Salazar of UT Southwestern Hospitals said on Monday that Peverley was treated "successfully" for a cardiac event at American Airlines Center.
"We provided oxygen for him," Salazar said. "We started an IV. We did chest compressions on him and defibrillated him, provided some electricity to bring a rhythm back to his heart, and that was successful with one attempt, which is very reassuring.
"As soon as we treated him, he regained consciousness. He was able to tell me where he was."