Prime Minister Hubert Minnis said the deaths were confirmed at the north-eastern Abaco Islands, which bore the brunt of the storm.
Some 13,000 houses are feared damaged or destroyed, according to the International Red Cross.
Dorian, the second-strongest Atlantic hurricane on record, remains "extremely dangerous", Mr Minnis said.
Pictures showed surging floodwaters, upturned cars and snapped trees.
Eyewitness videos and reports paint a picture of massive and widespread flooding, with panicked families fleeing to their roofs to escape rising floodwaters.
