The overcrowded boat from Teknaf, on Bangladesh's southern tip, was believed to be carrying about 110 people when it capsized 15 kilometers (9.5 miles) off the coast in the Bay of Bengal, according to officials.
"So far, 51 people have been rescued by coast guard, fishing boats and the border force's sea patrols," Lieutenant-Colonel Mohammad Jahid of Bangladesh border guards force said.
Jahid said rescuers are continuing to search for other survivors. No bodies have been recovered.
Risky voyages to Malaysia have become more frequent as Bangladeshi workers take to the seas seeking better jobs. Rohingya refugees fleeing persecution from Myanmar's Buddhist majority are also frequent sea travelers within Southeast Asia.
A Malaysia-bound boat carrying at least 120 people sank on October 28. Only six survived.
The number of Rohingyas attempting to escape Myanmar has grown with an increase in violence directed at Muslims in Rakhine state.
Violence since June has killed up to 200 people, and thousands of Rohingyas have lost their homes. Myanmar considers the 800,000 Rohingyas there illegal Bangladeshi immigrants and refuses them citizenship.
Since 1992, Bangladesh has refused to give Rohingyas refugee status, regularly turning back people attempting to escape Myanmar.
mkg/kms (dpa, Reuters)