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 15:00 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.
At least 20 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.
About 25,000 people are currently without electricity, energy provider Florida Power and Light reported.
The western Gulf coast is expected to be worst affected, with cities such as Tampa and St Petersburg in the path of the storm.
Queue at shelter in Estero, FloridaImage copyright Reuters
Image caption Shelters are filling up quickly and people are queuing to get inside
Media captionWatch: The Floridians who won't leave
And there are fears that storm surges combined with high tide on Monday could overwhelm some low-lying areas.
Florida Governor Rick Scott issued a stark warning to those in threatened areas.
"Look, it's getting late," he told NBC. "If you're not on the road on the west coast by noon [16:00 GMT], you need to get to a shelter, get to a friend's house if you're in an evacuation zone. Get off the road."
He said that storm surges in coastal areas could be as high as 12ft (3.7m), adding that people "cannot survive this".
Some 50,000 people have gone to shelters throughout the state, the governor said. Media reports say shelters in some areas have been filling up quickly and some people have been turned away.
Miami city and Broward county have imposed curfews to help clear the roads of traffic.
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