Fleeing Rohingya refugees have reported killings, rape and arson on a large scale.
Authorities there deny this, insisting that they have been waging a legitimate counter-insurgency operation after attacks by Rohingya militants on security forces last August.
A member of a Rohingya family is issued with her ID card.
Rights groups are expressing scepticism over the announcement that Myanmar has repatriated the first Rohingya family, despite warnings from the UN.
A Facebook post on the official page of Burma's Information Committee appears to show the family getting health checks and receiving packages of rice, mosquito netting and blankets.More news: Commonwealth Games: 'Ronaldo' spotted on bowling green
Bangladesh and Myanmar vowed to begin repatriation in January but the plan has been repeatedly delayed as both sides blame the other for a lack of preparation.
The Rohingya are viewed as one of the most persecuted communities in the world.
In a statement, the government said, five members of a Muslim family came to the Taungpyoletwea reception centre in Rakhine yesterday.
The agreement, signed by UN High Commissioner for Refugees Filippo Grandi and Bangladesh Foreign Secretary Md Shahidul Haque, established a framework of cooperation between UNHCR and Bangladesh on the safe, voluntary, and dignified returns of refugees in line with worldwide standards.
The UNHCR also urged the Myanmar Government to immediately provide full and unhindered access to refugees places of origin in Rakhine, which would enable it to assess the situation and provide information to refugees about conditions in the places of origin, as well as to monitor any possible future return and reintegration of refugees. "The repatriated Rohingya family did not reach Bangladesh as they used to live on no-man's land", Kamal said while talking to reporters this noon. The Rohingya family had been living in a camp erected on a patch there [between the two countries].More news: Brooke Henderson makes it # 6 at Lotte Championship
The United Nations has warned that a mass repatriation of Rohingya would be premature.
"Right now, the conditions are not conducive to a voluntary, dignified and sustainable return", Ursula Mueller, assistant secretary general for the UN's Office for the Coordination of Humanitarian Affairs, told AFP earlier this month after a visit to Rakhine.
The Rohingya are reviled by many in the Buddhist-majority country, where they are branded as illegal "Bengali" immigrants from Bangladesh, despite their long roots in Rakhine state.
Many have refused to take part in repatriation until they receive guarantees about their rights and citizenship.
Meanwhile boats carrying Rohingya from Rakhine state continue to leave Burma.More news: Memo warning Apple employees about leaking gets leaked to the me