Burma has accepted what appears to be the first five among some 700,000 Rohingya Muslim refugees who fled to neighbouring Bangladesh to escape military-led violence against the minority group.
The family returned even though the United Nations says it is not yet safe for them to return home.
A government statement said that five members of a family returned to western Rakhine state from the border area.
The statement said authorities determined whether they had lived in Burma and provided them with a national verification card.
The card is a form of ID, but does not mean citizenship - something Rohingya have been denied in Buddhist-majority Burma, where they have faced persecution for decades.
It said that the family was staying temporarily with relatives in Maungdaw town, the administrative centre close to the border.
The statement did not say if any more repatriations are being planned. Bangladesh has given Burma a list of more than 8,000 refugees to begin the repatriation, but it has been further delayed by a complicated verification process.
The two countries agreed in December to begin repatriating them in January, but they were delayed by concerns among aid workers and Rohingya that they would be forced to return and face unsafe conditions in Burma.
Hundreds of Rohingya were reportedly killed in the recent violence, and many houses and villages burned to the ground.
The United Nations and the US have described the army crackdown as "ethnic cleansing".
On Friday, the UN refugee agency and Bangladesh finalised a memorandum of understanding that describes the repatriation process as "safe, voluntary and dignified ... in line with international standards".