The confirmation comes despite United Nations warnings that it was not yet safe for families to return.
A statement posted on the Facebook page of the Information Committee on Saturday said
"The five members of a family... came back to Taungpyoletwei town repatriation camp in Rakhine state this morning."
A man, two women and two children were also photographed getting medical checks and ID cards.
They are now believed to be staying "temporarily" with relatives in Maungdaw town.
Official repatriation was due to start in January but this is the first family to return.
Hundreds of thousands of Rohingya fled Myanmar's Rakhine State to refugee camps in Bangladesh following violence in August which the UN has labelled ethnic cleansing.
Many have refused to take part in repatriation until they receive guarantees about their rights and citizenship.
It reported Saturday's returnees were provided the with National Verification Cards, a form of ID that falls short of citizenship and has been rejected by Rohingya leaders.
No further information has been given about other possible repatriations.
Repeat concerns have been raised by rights groups about repatriating the thousands who fled before their safety can be guaranteed.
On Saturday the UN's refugee agency said in a statement that conditions "are not yet conducive for the voluntary, safe, dignified, and sustainable return of refugees".
Satellite evidence published by Amnesty International also shows many Rohingya settlements have been bulldozed, with military installations built on some of the sites.
