The non-binding measure was adopted by consensus in the 193-nation assembly on Monday, a month after it was approved by the assembly's rights committee.
The resolution expresses "serious concern" over the plight of the Rohingya in Rakhine state, where 140,000 people live in squalid camps after violence erupted between Buddhists and Muslims in 2012.
Under a controversial government-backed plan, the Rohingya would be forced to identify themselves as “Bengali” - a term seen as disparaging - in order to apply for citizenship. Those who refuse would be forced to live in camps.
Many in Myanmar's government and local Buddhists view Rohingya as illegal immigrants from neighbouring Bangladesh, but the community maintains its has ancestral roots in the country.
The resolution urges the government to protect the rights of all inhabitants of Rakhine State and allow "equal access to full citizenship for the Rohingya minority," to "allow self-identification" and ensure equal access to services.
The measure drafted by the European Union was adopted by consensus after Myanmar did not request a vote on the measure. A vote is held if the country targeted by the resolution requests it.
Despite criticism of the Rohingya's treatment, the resolution welcomes "continued positive developments in Myanmar" toward reform and notes that the government is making efforts to address the "complex situation in Rakhine State."
It calls for an office of the UN High Commissioner for Human Rights to open "without delay" in Myanmar.