Boats carrying passengers from low-lying, makeshift camps were evacuating people Monday ahead of Cyclone Mahasen, expected to make landfall this week, Voice of America reported Tuesday.
The U.N. Office for the Coordination of Humanitarian Affairs said at least one of five boats carrying about 100 people struck rocks near Myanmar's Rakhine state.
It said at least 42 people survived the crash.
A search-and-rescue operation has begun.
Tens of thousands of Rohingya Muslims are living in camps in Rakhine after they were displaced last year because of violence between the state's Muslim and Buddhist populations.
"It appears that this boat left the camp with the blessing of the authorities before hitting rocks," Barbara Manzi, head of the U.N. Office for the Coordination of Humanitarian Affairs, told the BBC.
Officials began evacuations this week after warnings the cyclone may hit Bangladesh and causing heavy rain and flooding in western Myanmar, formerly known as Burma, that would affect the estimated 140,000 displaced people -- mostly Rohingya -- living in makeshift shelters in Rakhine, aid groups said.
"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."
In a statement Tuesday, Human Rights Watch said if Myanmar failed to evacuate all those at risk, any disaster "will not be natural, but man-made."