An official statement said a family of five returned to Rakhine state from a camp in Bangladesh. They had been provided with national verification cards, but that does not make them citizens. The Rohingya have long been denied that status in Buddhist-majority Burma.
The family was staying with relatives close to the border.
Bangladesh has given Burma a list of more than 8,000 refugees to begin repatriations. They were meant to begin in January, but there were delays by concerns about unsafe conditions in Burma.
Many Rohingya have been killed and their villages burned -widely seen as ethnic cleansing.
On Friday, the UN refugee agency and Bangladesh finalized a memorandum of understanding on a repatriation process, though the United Nations "considers conditions in Burma are not yet conducive for returns."
Burma Social Welfare Minister Win Myat Aye met refugees in Bangladesh for more than an hour last week.
Rohingya leader Abdur Rahim said at least eight rape victims were among those who met him. He also said people became angry when Win Myat Aye said the Rohingya must accept ID cards that state they are migrants from Bangladesh.