Popularly known as "Ahok", he is accused of insulting the Koran while campaigning in governorship elections.
Mr Purnama is a Christian from the Chinese ethnic minority and the first non-Muslim to lead the city.
The case has prompted fears of a rise in tensions in the largely Muslim country.
The naming of Mr Purnama as a suspect means prosecutors can bring him to trial. If found guilty he faces up to five years in prison.
