Basuki Tjahaja Purnama, popularly known by his Chinese name Ahok, is accused of insulting the Koran.
Mr Purnama has apologised for the offending remarks but denies committing blasphemy, which carries a maximum five year jail sentence.
The case is being seen as a test of religious tolerance in Indonesia.
Mr Purnama is the city's first non-Muslim governor in 50 years and there are some who fear the trial signals the growing influence of hardliners in the world's largest Muslim majority nation.
