Local fisherman managed to rescue about 50 passengers from the sea where the ship went down at 3 a.m. Wednesday around 25 miles into the Bay of Bengal near the border with Myanmar, Bangladeshi media said.
Later, vessels from the coast guard, Border Guard Bangladesh and the navy joined in the search, a report by The Daily News said.
At least two of the survivors are Rohingya, officials said.
Lt. Col. Jahid Hasan of the Border Guard said the boat left the area around Teknaf on the southern tip of Bangladesh around midnight.
Passengers told Border Guard officials that the problem started when the boat turned too sharply to search for a passenger who had fallen overboard and the vessel capsized.
One of the passengers claimed passengers had paid middlemen $370-$620 for the voyage to Malaysia. If a passenger were to find a job in Malaysia, they were to pay another $1,850 to the middlemen, the passenger said.
Bangladeshi maritime authorities have been alert in the coastal areas around Teknaf and up the coast past Cox's Bazar since communal troubles erupted across the border in Myanmar's Rakhine state in June.
Thousands of Muslim Rohingya have flooded across the border to escape violence between Muslims and Buddhists.
The government of Myanmar claims the Rohingya aren't citizens of Myanmar and the Bangladeshi government looks upon them as refugees from Myanmar and houses them in camps with help from international aid organizations.
Many Rohingya leave Myanmar and enter Bangladesh looking for a better life which could include paying people smugglers for passage in unseaworthy vessels to Malaysia, Thailand and other Southeast Asia countries.
The Daily News reported that Bangladeshi maritime authorities also arrested 59 people, mostly Rohingya, from Teknaf and surrounding areas in a crackdown on illegal migrants this week.
Fatal accidents like this week's tragedy have happened before in the area popular with people smugglers for launching their unseaworthy ships with human cargo.
In December around 30 migrants drowned when a ship carrying 130 people capsized off the coast near St. Martin's Island, a popular tourist destination where fishing is main occupation for the population of around 5,500.
The 3-square-mile island is also a stopping off point for illegal migrants from Myanmar, around 5 miles away.