Fishermen in the region have been taking precautions
Hurricane Emily has battered the eastern Caribbean island of Grenada, ripping off roofs and flooding streets.
Nearly 2,500 people fled to shelters, while others stayed at home with stockpiles of canned food and water.
Grenada is still recovering from the more powerful Hurricane Ivan last year, which destroyed 90% of homes.
The hurricane moved quickly away from the Windward Islands, and has strengthened as it heads west towards Jamaica and the Gulf of Mexico.
As of 2100 GMT, it was located about 445 miles (720km) southeast of Santo Domingo in the Dominican Republic.
The US National Hurricane Center said Emily had been upgraded to Category 3, which encompasses winds of up to 130mph, and was now the second major hurricane of the season.
If it continues to follow its current course, it is expected to pass south of Jamaica on Saturday, cross Mexico's Yucatan peninsula early on Monday and enter the Gulf of Mexico early on Tuesday.
The Jamaican government has issued a hurricane watch, while tropical storm warnings are in force in parts of the Dominican Republic, Haiti and Venezuela.
According to the Pennsylvania-based forecasting company AccuWeather, the bulk of US oil and gas platforms in the gulf should not be affected.
Earlier, the Venezuelan authorities ordered oil tankers and other vessels to stay in port.
There are still fears that Venezuela and the Antilles islands of Bonaire, Curacao and Aruba might be affected by heavy rain, triggering deadly flash floods and mudslides.
Grenada bears the brunt
A Grenadian disaster official, Sylvan McIntyre, told the BBC there were no reports of casualties so far, but he said there had been "significant damage" to houses.
According to reports, the hurricane destroyed the roof of the only hospital on the island of Carriacou, north-east of the main island.
In the Grenadian capital, St Georges, the storm also blew away the roof of the operating theatre at the main hospital and destroyed the roofs of two police stations in St Georges and Grenville.
"They [Grenada] took a major portion of the brunt of the storm," said Trisha Wallace, a forecaster with the US Hurricane Center in Miami quoted by Associated Press news agency.
Grenada has not been able to prepare thoroughly for this year's hurricane season as it is still trying to rebuild following Hurricane Ivan, which killed nearly 40 people in September.
Many buildings still do not have roofs, partly because of a shortage of building materials. Officials have said it could take up to 10 years to recover.
Hurricane projections often change because of the unpredictable nature of storms. Emily had been downgraded to a tropical storm by forecasters on Wednesday, but as the storm gathered strength it was again boosted to a hurricane.
Emily follows closely behind Hurricane Dennis, which caused more than two dozen deaths as it rampaged over Haiti, Jamaica, Cuba and Florida.