The victims, many of whom had been living in camps after being displaced by the Buddhist-Muslim violence, were being evacuated in a boat Tuesday to escape the approaching Cyclone Mahasen when their craft capsized.
The Los Angeles Times, quoting the United Nations Information Center in Myanmar, said at least 58 of the 100 people on board the boat were missing or feared drowned.
Aye Win, a spokesman at the center, said the boat may have struck rocks off Pauktaw town in Myanmar's western Rakhine state.
Rakhine is home to most of the country's Rohingya Muslim minority. Myanmar, formerly called Burma, has been the scene of communal violence between the majority Buddhists and the Rohingya Muslims in Rakhine state since last year. Thousands of the Rohingyas, who fled the violence, have since been living in camps.
The BBC reported about 50 people were feared to have drowned.
The report said more than 40 survivors had been found.
The evacuation began after a warning that many of the low-lying areas, where the displaced people are living in camps, faced flooding from the cyclone.
The BBC quoted Myanmar authorities as saying the evacuation involved moving about 130,000 people to higher grounds.
Cyclone Mahasen could approach the coast of western Myamar and neighboring Bangladesh as early as Thursday.
"The government has been repeatedly warned to make appropriate arrangements for those displaced in Rakhine state," Isabelle Arradon, deputy Asia Pacific director of Amnesty International, said in a statement Monday. "Now thousands of lives are at stake unless targeted action is taken immediately to assist those most at risk."
Human Rights Watch also criticized the Myanmar government.
"The Burmese government didn't heed the repeated warnings by governments and humanitarian aid groups to relocate displaced Muslims ahead of Burma's rainy season," Human Rights Watch's Asia Director Brad Adams said in a statement. "If the government fails to evacuate those at risk, any disaster that results will not be natural, but man-made."
The organization said among the displaced population are tens of thousands of "unregistered" Rohingya who have not been formally recorded by Myanmar authorities. It said the unregistered Rohingyas have repeatedly told humanitarian aid groups that they lack food, shelter, medicine, potable water, clothing, and other necessities.
The Myanmar government in a statement Monday said the National Disaster Preparedness Central Committee led by Vice President Nyan Tun had made preparations ahead of the storm, Burma News International reported. The military and emergency rescue teams have been readied, the report said.