Tickets went on sale Monday for the shows being held at the Sony Centre for the Performing Arts at 8 p.m. and 11 p.m. tomorrow.
By late Monday evening, tickets appeared to be quickly dwindling. Just before 9:30 p.m., the Ticketmaster website indicated that there were "not many left" for the early-and-late shows.
The back-to-back shows on Tuesday are part of a tour in which Prince has been announcing his performances at the last minute.
The two shows come six months after Prince fans lined up for a rumoured show that never materialized at Massey Hall.