US officials have said the hurricane was "potentially catastrophic"
Hurricane Irma, which is heading towards the Caribbean and southern United States, could bring winds of 185mph (300km/h).
The US National Hurricane Centre said Irma was "potentially catastrophic" and tweeted that it was "the strongest hurricane in the Atlantic (Ocean) outside the Caribbean Sea and Gulf of Mexico in NHC records".
The hurricane was upgraded to a category five storm - the highest possible designation - on Tuesday afternoon.
Irma's eye is forecast to cross the northern Leeward Islands, east of Puerto Rico, on Tuesday night or early Wednesday and is expected to reach southern Florida on Saturday.
The Governor of Florida, Rick Scott, has declared a state of emergency, asking President Trump to make a "pre-landfall" emergency declaration.
There are fears that Irma could be be even stronger than Hurricane Harvey when it hits land.
Hurricane Harvey, a category four storm at its strongest, had maximum sustained winds of more than 200 km/h just before it made landfall in Texas, killing more than 60 people and leaving 30,000 homeless.
The US National Oceanic and Atmospheric Administration (NOAA) is warning that Irma's winds could strengthen further in the next 48 hours as it approaches the Caribbean.
The latest advisory from the National Hurricane Center is that it will score a direct hit on the island of Barbuda at 7am Irish time on Wednesday, followed by another direct hit on Anguilla, a British overseas territory, at 7pm Irish time the same day.
There is a chance it will go on to hit or pass very close to Florida at the weekend. It is expected to bring around half a metre of rain there.
Forecasters have said Irma is a classic "Cape Verde hurricane" which forms in the far eastern Atlantic near the Cape Verde Islands and then moves all the way across the Atlantic.
Antigua and Barbuda Prime Minister Gaston Browne has ordered workers to clear drains and prune trees as branches could down power lines in strong winds.
"The passage of a hurricane is not a matter to be taken lightly, but we must not panic," he said.
Governor of US territory Puerto Rico, Ricardo Rossello, said 10-20cm of rain was expected, as well as winds of 65-80 km/h as he warned of flooding and power cuts.
A state of emergency was declared on the island, which has a population of about 3.4 million.
Ronald Jackson, head of the Caribbean disaster emergency management agency, said: "We're looking at Irma as a very significant event.
"I can't recall a tropical cone developing that rapidly into a major hurricane prior to arriving in the central Caribbean."
Florida governor Rick Scott urged the state's residents to ensure their disaster supply kits were ready.
"FL (Florida) knows how important it is to be prepared. Encourage your loved ones to have a plan ahead of any potential storm," he tweeted.