"Myanmar faces a very serious crisis -- with a potentially severe impact on the security of the region," UN High Commissioner for Human Rights Zeid Ra'ad Al Hussein said during a speech in Jakarta.
His remarks follow the publication of a report last week about mass graves of Rohingya in Myanmar's crisis-hit Rakhine state, where government troops have been accused of waging an ethnic cleansing campaign against the minority.
Myanmar denied the mass grave report and wider allegations of rights abuses, saying it launched a proportionate crackdown on Rohingya rebels.
But it has blocked reporters and UN investigators from independently accessing the conflict zone and investigating refugee claims about a genocide.
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Zeid on Monday said Myanmar had enjoyed strong growth including a focus on socio-economic development in the Rakhine region, but that this could not mask "institutionalised discrimination" against the minority.
The UN rights chief is due to meet with Indonesian President Joko Widodo as well as top government officials and rights groups during his three-day visit.
Parliament is set to pass a long-dormant bill to make sex outside marriage illegal. Gay marriage does not exist in Indonesia, meaning homosexual relations would be effectively outlawed.