The boat grounded on Saturday near Mangrove Cay, Andros Island, in heavy seas caused by Tropical Storm Isaac.
Officials have ordered a search of the nearby waters as they fear more migrants may have been on board and could have drowned.
In June, 11 Haitians died when their boat capsized off the Bahamas.
The survivors told officials at least 170 people had been aboard the boat.
They said they had left Cap-Haitien, in Haiti, on 18 August.
Doctors said the migrants were in good health, except for some who showed signs of dehydration.
It is not clear whether they were heading to the Bahamans or if their final destination was the United States.
Fatal accidents at sea involving migrants from Haiti, the Western hemisphere’s poorest nation. are not uncommon.
In December, 38 migrants were found dead after their boar sank just off the eastern tip of Cuba.
And in 2009, US Coast Guard officials called off their search for about 70 migrants from Haiti whose boat capsized off the Turks and Caicos Islands.