People living in the coastal strip south of the Bangladesh port of Cox's Bazar fished 37 survivors out of the water and 11 have been admitted to hospital in a critical condition, Mohammad Abul Khair, the officer in charge at Ukhiya police station, said.
The boat had keeled over in choppy seas as rain fell. According to survivors they had paid 50,000 kyat ($37) to be taken to Bangladesh. They had abandoned their homes in Buthidaung, in the strife-torn north of Myanmar's Rakhine State.
More than 600,000 Rohingya have fled to neighbouring Bangladesh since August.
United Nations officials have described the Myanmar military's action as "ethnic cleansing", an accusation that Myanmar denies.
Many of the Rohingya refugees have made the precarious sea and river crossing to reach the safety of predominately Muslim Bangladesh, though dozens have drowned making the attempt.
People look at a boat that capsized with a group of Rohingya refugees in it at Bailakhali, near Cox's Bazar, Bangladesh
Four Rohingya Muslims, a man, woman and two children, drowned when a small wooden fishing boat carrying dozens of refugees fleeing ethnic violence in Myanmar capsized off the Bangladesh coast on Tuesday, police said.
