The challenger Issa Tchiroma Bakary declares himself the winner of Sunday's presidential election in the West African country, which has been ruled by Biya since 1982.
"Our victory is clear. It must be respected", writes Tchiroma in a post on Facebook.
An official election result is not expected until two weeks from now.
Cameroon is plagued by internal conflicts and unrest at the border with Nigeria. Almost half of the country's population lives in poverty, according to the UN.