Cameron Paterson, 17, posted the obscene message mocking the ex-Aston Villa and Bulgarian player shortly before he retired as a player after suffering cancer.
Paterson, of Dalmuir, West Dunbartonshire, admitted at Kilmarnock Sheriff Court that he sent an offensive and sectarian message last April. He was fined £360.
The message included the words: "Petrov a hope you die" and used a derogatory sectarian comment. Petrov, 33, retired last May as captain of Aston Villa, having successfully fought acute leukaemia. He took a new coaching role with the club but left last August, saying he wanted more time with his family.