The Devon club reported the operation had been a success after Perryman, Tottenham's appearance record holder and capped once by England, was taken ill during Saturday's 2-2 League One draw with Sheffield United at St James Park.
Perryman was experiencing shortage of breath during the game.
The club on Sunday released a statement on their website, which read: "Last night, Steve Perryman was transferred from the RD&E (Royal Devon & Exeter) Hospital to Derriford Hospital in Plymouth where he underwent heart surgery.
"This morning the surgery was reported as successful.
"Needing complete rest, Steve will not be contactable until further notice.
"On Steve and his wife Kim's behalf, we would like to say thank you for all the kind messages of goodwill."