The boat was believed to be taking the Rohingya from Myanmar's western state of Rakhine to Malaysia, where thousands of members of the Muslim minority have sought sanctuary since violent clashes with Buddhists erupted last year.
"Altogether 66 people -- 38 men and 28 women -- were on board when the boat capsized," a police official in Rakhine told AFP, adding six survivors had been found in the Bay of Bengal.
The missing are thought to have been IDPs (internally displaced persons) from the area around the state capital Sittwe, the officer added, requesting anonymity.
Thousands of Rohingya have fled Myanmar since then, many paying smugglers for passage on rickety and overcrowded boats to Malaysia or further south, despite the dangers posed by rough seas in the Bay of Bengal.
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Hundreds are believed to have died at sea so far this year.
In May nearly 60 Rohingya Muslims went missing after their boat sank after hitting rocks as a cyclone approached the bay.
Myanmar views its population of roughly 800,000 Rohingya as illegal immigrants from neighbouring Bangladesh and denies them citizenship.
Rohingya boats frequently make landfall in Thailand, where those passengers caught by authorities are detained. According to rights groups they are vulnerable to exploitation by human traffickers.
The United Nations has raised fears that the number of Rohingya fleeing camps for the displaced will rise further this year.
It has urged Myanmar's reformist government to address the humanitarian crisis by easing sectarian divisions in the area and improving conditions in the squalid camps where tens of thousands languish.
The UN High Commissioner for Refugees in Geneva said Friday it had received "worrying reports" that around 1,500 people had left the Rakhine area in recent days as the annual sailing season gets underway.