The measure was adopted by consensus in the General Assembly's rights committee following some wrangling with countries from the 57-nation Organisation of Islamic Cooperation or OIC, which had sought stronger language.
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 neighboring 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.
Myanmar's representative voiced opposition to the use of term "Rohingya" in the resolution and warned this would stoke tensions in Rakhine State.
"Use of the word by the United Nations will draw strong resentment from the people of Myanmar, making the government's effort more difficult in addressing this issue," said the delegate.
The representative emphasized that the government was seeking to address the issue.
The measure drafted by the European Union now moves to the full Assembly, where it is likely to be adopted again by consensus. 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.