Stars general manager Jim Nill says Peverley was released from the Cleveland Clinic on Wednesday, a day after surgery.
Peverley is expected to return Thursday to Dallas. He will be monitored closely and may require further treatment.
The 31-year-old Peverley chose for less invasive treatment after an irregular heartbeat was diagnosed during training camp.
Nill says there is "no decision being made at this time" on if Peverley will play hockey again. He is out this season.
Peverley collapsed during the first period March 11 against Columbus. The game was postponed and will be made up April 9.