Hurricane Matthew, a category-four, brought winds of 150 mph as it moved across the region last night, and is set to bring up to 64cm of rain as it moves towards Jamaica, Haiti and eastern Cuba.
Flood waters have blocked roads in Jamaica’s capital Kingston, with parts of the country lashed by rain and strong winds, the BBC said.
A hurricane warning is in place for Haiti, and authorities have urged people to stock up on food and water. Thousands still live in tents following the devastating earthquake in 2010.
Forecasters have also predicted that the storm could pass east of Florida through the Bahamas.
The Jamaican government urged people to evacuate and prepare for the storm two days ago.
Minister of local government Desmond Mackenzie said: "No turning back now. It is a matter of how long we have to wait this out."