High winds and heavy rains are lashing western Cuba as Hurricane Wilma strengthens to a Category Three storm and heads for Florida.
Florida officials have warned people to leave or take shelter from Wilma
It finally left Mexico's Gulf coast on Sunday after pounding the Yucatan peninsula, killing at least six people.
The Cuban government says more than 600,000 people have been moved from coastal areas, where several villages have been flooded by big storm surges.
Florida residents who have refused to leave have been urged to take shelter.
Wilma has strengthened to a Category Three storm, after weakening as it lingered for 48 hours over Mexico, and is packing 115mph (185km/h) winds, forecasters said.
The hurricane is expected to reach the south-west coast of Florida on Monday morning, the National Hurricane Center (NHC) said.
Tropical force winds are already battering western Cuba and moving nearer to the Florida Keys, forecasters added.
Florida Governor Jeb Bush had appealed on Sunday for people to leave the low-lying island chain, after it appeared many of its 80,000 residents had chosen to ignore the warnings.
"I cannot emphasise enough to the folks that live in the Florida Keys a hurricane is coming, and a hurricane is a hurricane and it has deadly force winds," he said.
Forecasters have warned the storm could bring storm surge flooding 2.7 to 5m (nine to 17ft) above normal levels on Florida's south-west coast and trigger tornadoes.
It is then expected to "take off like a rocket" up Florida's Atlantic coast, NHC director Max Hayfield said, threatening cities like Miami and Fort Lauderdale.
Meanwhile in Cuba, people living in some coastal areas said a storm surge had dumped fish on roads several hundreds yards inland.
The island has already been lashed by rains and tornadoes while Wilma pounded Mexico - and Cuba's chief meteorologist has warned people that the worst is yet to come.
The storm tore roofs off buildings on Mexico's Yucatan Peninsula
There are reports that some villages have been cut off, and at least seven people were injured by the tornadoes, which destroyed up to 20 homes.
Earlier, officials in Mexico said Wilma had destroyed thousands of homes and hotels on the Yucatan Peninsula during its two-day onslaught.
The army and navy are planning to drop aid supplies for the tens of thousands of people in overcrowded shelters.
It is only now that locals and the emergency services can really get out to see what destruction Wilma left behind, says the BBC's Claire Marshall in the resort of Cancun.
The slow-moving storm sent waves surging over hotels in Cancun, wiped out electricity supplies and flattened hundreds of homes. There were reports of looting amid the destruction.
At least two people died on Cozumel island and four on the mainland, officials said.
Haiti and the Dominican Republic were earlier drenched by torrential rains brought by Tropical Storm Alpha, now downgraded to a tropical depression.
Forecasters warn Alpha, whose formation made this year's Atlantic hurricane season the most active since 1933, could strengthen again.
It is the first time the NHC has had to resort to the Greek alphabet to name a storm, after all 21 names pre-assigned for storms this year were used up.
The hurricane season still has five weeks to run. It ends on 30 November.