By Deutsche Presse Agentur
Local government official Mohammad Ali said the boat, which had been carrying 35 Rohingyas, overturned near Jadimura Point on the Naf River, which separates Bangladesh from Myanmar.
"Three of them could be rescued after they swam into Bangladesh territory, while the rest of the passengers could not be traced," Ali told reporters, citing one of the survivors.
The accident occurred more than 370 kilometers south-east of the Bangladeshi capital, Dhaka.
Border Guard Bangladesh (BGB) officer Abuzar Al Jahid said he heard about the accident and the subsequent rescue operation by the local residents.
Paramilitary troopers put on alert on the Myanmar frontier have prevented at least 40 Rohingyas trying to cross the border by boat just on Monday, he said.
The United Nations estimates that more than 10,000 Rohingyas entered Bangladesh in the past weeks to flee violence in neighbouring Myanmar's Rakhine state, which has claimed more than 100 Rohingyas.
Nearly 29,000 Rohingya who have been documented as refugees have been living in two squalid camps in the Bangladeshi district of Cox's Bazar since the 1990s. They were all driven out of Myanmar.
The number of undocumented Rohingya living in Bangladesh is estimated to stand at somewhere between 200,000 and 500,000.