The migrants appeared to be aiming for US shores and the incident happened less than 240km from Miami, said Ralph McKinney, chief petty officer with the Royal Bahamas Defence Force.
Two Haitian survivors, a man and a woman, were being treated at a Nassau hospital for dehydration.
The third survivor, a Honduran marine mechanic, was taken into police custody as the authorities investigated smuggling allegations, McKinney said.
The two Haitian survivors identified the Honduran as the sunken vessel's captain, said Chris Lloyd, of the Bahamas Air Sea Rescue Association.
Three US coast guard helicopters, the Bahamas military and its volunteer air-sea rescue service searched for more survivors on Monday, witnesses said.
The US coast guard has been on alert for a spike in migration following riots earlier this month over escalating food prices in Haiti, the poorest country in the Western hemisphere.
So far this year, 737 Haitians have been intercepted, compared to 1,583 for 2007, according to the coast guard.
Louis Harold Joseph, Haiti's ambassador to the Bahamas, said he had not yet received confirmation that everyone who died was Haitian.
He expressed doubts that the voyage was connected to the Haitian food riots, in which at least seven people died.
Survivors described the capsized vessel as a fast boat, suggesting the migrants had more money than others who make the perilous crossing jammed on board makeshift vessels.
Last year, a migrant boat capsized near the Turks and Caicos islands, pitching Haitians into shark-infested waters and killing at least 61 people.