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.
After moving slowly along the northern Cuban coast it is now heading out to sea towards Florida.
At 21:00 GMT, Irma had maximum sustained winds of 200km/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.
At least 24 people are so far known to have died as Hurricane Irma progressed across the Caribbean throughout the week.
What is happening in Florida?
Irma is expected to hit the coast at around lunchtime on Sunday, but the outer bands are already affecting the south of the state and central Miami is being lashed by heavy rain.
The Florida Keys - a chain of small islands to the south - have suffered some minor damage and are expected to bear the brunt of the storm on Sunday morning.
The head of emergencies agency Fema, Brock Long, told CNN there were "no safe areas within the Keys".
"You put your life in your own hands by not evacuating," he added.