Around one million people have been left without power and one person has been killed after Hurricane Ian lashed Cuba.
Cuba-focused media outlets have also reported damaged buildings across the country.
The category three hurricane, packing wind speeds of up to 195km/h (120mph), is now heading for Florida and is expected to strengthen.
Parts of Florida have not faced such an intense hurricane in about a century.
As of 21:00 GMT on Tuesday, the hurricane was growing stronger in the south-eastern Gulf of Mexico and moving north at 10mph, the US National Hurricane Center (NHC) reports.
The storm is expected to pass over the Florida Keys on Tuesday night before approaching Florida’s west coast on Wednesday.
The NHC said in its bulletin that Ian could be a category four hurricane by that point, with wind speeds topping 130mph. Over two million people in Florida are under evacuation orders.
In Cuba, forecasters had warned that some regions could see up to 30cm (12in) of rain from Hurricane Ian.
Mayelin Suarez, a resident of Pinar del Rio, called the night the storm hit “the darkest of her life”.
“We almost lost the roof off our house,” she told Reuters. “My daughter, my husband and I tied it down with a rope to keep it from flying away.”
Cuban President Miguel Diaz Canel visited the area and vowed that the province would rise “above adversity”, the Cuban presidency tweeted.
A 43-year-old woman in the province was killed after the walls of her home collapsed.
Cuban authorities declared emergencies in six areas, with forecasters warning of storm surges on the coast, along with flash floods and mudslides.
Florida Governor Ron DeSantis warned in a news conference on Tuesday that the storm is “the real deal”.
The governor declared a state of emergency for all of Florida over the weekend and has activated 5,000 National Guard troops to assist with relief efforts.
Along Florida’s Tampa Bay coast, grocery store shelves were quickly cleared of basic necessities and there were long queues at gas stations.
The Tampa area could receive its first direct hit from a hurricane since 1921, officials say, and might see 3m (10ft) of storm surge along the coast.
Local officials in Tampa, Miami and Fort Lauderdale are distributing free sandbags to help residents protect their homes from flooding.
Meteorologists have said flash flooding is possible by Tuesday in the Florida peninsula and Florida Keys as the hurricane approaches.