Coast guard and border guard officials said the boat was overloaded with about 100 people when it sank in the mouth of the Naf river that separates Myanmar from Bangladesh.
Coast guard and border guard officials said the boat was overloaded with about 100 people when it sank in the mouth of the Naf river that separates Myanmar from its South Asian neighbour Bangladesh.
"It capsized near (the coastal village of) Galachar with nearly 100 people. We recovered two dead bodies. Two people were rescued alive," area coast guard commander Alauddin Nayan told AFP.
Nayan said some 40 people in the boat were adult Rohingya Muslims fleeing their villages in Rakhine.
"The rest were children," he said, adding that the coast guard had launched a search and rescue operation.
Border guard boats rescued 11 more Rohingya including three women and two children after scouring the estuary of the Naf river, Abdul Jalil, a Border Guard Bangladesh official, told AFP.
"We spoke to several survivors. One of them said the boat was carrying on average 80-100 people including 30-35 males," he said.
Since the boat capsized near the Myanmar side of the border, Jalil said many may have swum to the Rakhine coast.
The coast guard said the boat sank at around 10:00 pm (1600 GMT).
Local media quoted a survivor as saying the boat sank due to high waves and bad weather.
Last week more than 60 Rohingya refugees were feared dead after a boat carrying them from Myanmar capsized in rough weather in the Bay of Bengal just off the Bangladesh coast.
The bodies of 23 people were retrieved, but the death toll was expected to surge to around 60, with many of the dead likely to be young children too weak to swim through the churning water.
Around 150 Rohingya, many of them children, have drowned while trying to reach Bangladesh in small fishing boats that coastguards say are woefully inadequate for the rough seas.
Nearly 520,000 Rohingya Muslims have fled Rakhine state for Bangladesh since late August, many by boat across the Naf river.
The refugee crisis erupted after Rohingya militant raids on Myanmar police posts on August 25 prompted a brutal military backlash.
The United Nations has said the army campaign could be "ethnic cleansing" while Myanmar military leaders have blamed the unrest on Rohingya.
Myanmar's government refuses to recognise the Rohingya as a distinct ethnic group and considers them illegal migrants from Bangladesh.
While the worst of the violence appears to have abated, insecurity, food shortages and tensions with Buddhist neighbours are still driving thousands of Rohingya to make the arduous trek to Bangladesh.
Bangladesh has made the journey even more difficult with a clampdown on boats running refugees across the Naf river.
Authorities have destroyed at least 30 wooden fishing vessels whose captains are accused of smuggling Rohingya and illegal drugs into the country.