Peverley, 31, missed the Stars' preseason schedule and season opener after undergoing treatment for an irregular heartbeat. He also missed a game last week.
Dr. Gil Salazar said Peverley responded quickly to treatment for a "cardiac event" Monday. "I was able to talk to him in the back of the ambulance and he was able to tell me where he was. He actually wanted to get back in the game," Salazar said at a news conference.
In a statement, the NHL said the game had been postponed "as a result of the emotional state of the players on both teams caused by the medical emergency." No date was set for the resumption.
The Stars were trailing, 1-0, when Peverley came off the ice and slumped over. His teammates banged their sticks against the boards and on-ice officials stopped the game at 6:23.
Coach Lindy Ruff said he spoke to Peverley, who wanted to know how much time remained in the period. "Typical athlete," Ruff said.