The club said a percentage of proceeds from the pie, which contains chicken, leek and Bulgarian kefta meatballs, will be donated to the Cure Leukaemia charity.
The 32-year-old Petrov, who has more than 100 international caps for Bulgaria, was diagnosed with acute leukaemia last month and has started treatment at a London hospital.
The Bulgarian Football Union dedicated this week's round of the domestic championship, played between Tuesday and Thursday, to Petrov with players wearing specially signed shirts in support of him.
Several league matches have been stopped in the 19th minute, Petrov's Villa shirt number, with the crowd applauding for a minute.
"There are ordeals in life in which we must be stronger than ever, and I think I have enough strength and faith to cope. I do believe that together we will win this match too," Petrov said on Friday as he continues his treatment.