Basuki "Ahok" Tjahaja Purnama cannot leave the country while the investigation is under way, officers said.
"After long discussions, we reached a decision that the case should be tried in an open court," said National Police chief detective Ari Dono.
The Islamic Defenders Front, a group which wants to impose Shariah law, began demanding Ahok's arrest after a video circulated online in which he joked to an audience about a passage in the Koran that could be interpreted as prohibiting Muslims from accepting non-Muslims as leaders.
The governor has apologised for the comment.
Earlier this month the capital Jakarta was rocked by a protest by conservative Muslims against the governor.
One person died and dozens were injured in rioting. More protests have been threatened if Ahok is not arrested.
Blasphemy is a criminal offence in Indonesia, where 90 per cent of people are Muslims.
Amnesty International documented 106 convictions between 2004 and 2014, with some individuals imprisoned for up to five years.
