Perryman 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.
An Exeter statement 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."
Tottenham also added their best wishes for Perryman, who holds the record for the most number of appearances for the club, after a 17-year career at White Hart Lane.
"The thoughts and best wishes of everyone at the Club are with Steve Perryman as he remains in hospital following heart surgery," the club said.