Florida's state governor has told residents ordered to leave their homes to go to shelters and avoid the roads as Hurricane Irma approaches.
Rick Scott said it was now too late to drive away from the danger areas.
After devastating several Caribbean islands, Irma is lashing Cuba with strong winds and heavy rain, and is due to make landfall in Florida on Sunday.
Some 6.3 million people, more than 25% of the US state's population, have been ordered to evacuate.
The hurricane made landfall on the Sabana-Camaguey Archipelago, in Cuba's north-east, late on Friday as a category five storm but has now weakened to a category three.
At 18:00 GMT, Irma had maximum sustained winds of 201km/h (125mph), the National Hurricane Center in the US said.
It was the first category five hurricane to hit Cuba in more than 80 years, and it is expected to strengthen again before reaching Florida.
Which other areas have already been hit?
At least 24 people are so far known to have died as Hurricane Irma progressed across the Caribbean throughout the week.
St Martin and St Barthelemy: Six out of 10 homes on St Martin, an island shared between France and the Netherlands, now uninhabitable, French officials say. They said nine people had died and seven were missing in the French territories, while two are known to have died in Dutch Sint Maarten
Turks and Caicos Islands: Widespread damage, although extent unclear
Barbuda: The small island is said to be "barely habitable", with 95% of the buildings damaged. Antigua and Barbuda Prime Minister Gaston Browne estimates reconstruction will cost $100m (£80m). One death has been confirmed
Anguilla: Extensive damage with one person confirmed dead
Puerto Rico: More than 6,000 residents of the US territory are in shelters and many more without power. At least three people have died
British Virgin Islands: Widespread damage reported, and four dead
US Virgin Islands: Damage to infrastructure was said to be widespread, with four deaths confirmed
Haiti and the Dominican Republic: Both battered by the storm, but neither had as much damage as initially feared