Hurricane Ian knocked out the power across Cuba and devastated some important tobacco farms as it hit the country's western tip on Tuesday.
Cuba's Electric Union said they were working over the night to gradually restore power to the country's 11 million people.
Ian was expected to get even stronger over the warm Gulf of Mexico, approaching the southwest coast of the US state of Florida.
The Category 3 hurricane packed a punch with winds of up to 130 miles (210 kilometers) per hour recorded at San Juan y Martinez, a small town on Cuba's southwest coast.
Authorities in Cuba's Pinar del Rio province evacuated 50,000 people ahead of the storm. Some 6,000 evacuees were staying in state run-shelters.
State-run media said 33,000 tonnes of tobacco from prior harvests in Pinar del Rio had been secured ahead of the storm. One of Cuba's most important tobacco farms in La Robaina was damaged due to the winds.
Rain and winds buffeted the capital, Havana, but the city was spared the brunt of Ian's impact.
"We almost lost the roof off our house. My daughter, my husband and I tied it down with a rope to keep it from flying away," street vendor Mayelin Suarez told Reuters.
Florida bracing for impact
The US National Hurricane Center expected Ian to strengthen to a Category 4 storm before hitting Florida late on Tuesday. That could mean top winds of 140 miles (225 kilometers) per hour.
Coastal residents emptied grocery shelves, boarded up windows and fled to evacuation shelters as Ian lashed Flordia's southern tip with tropical storm-force winds hours before it was forecast to make US landfall on Wednesday evening.
A hurricane warning has been extended to portions of far southwestern Florida as the storm's path veered slightly from previous predictions.
US President Joe Biden's administration declared a public health emergency for the state in anticipation of the storm's arrival.
"This is a really, really big hurricane,'' Florida Governor Ron DeSantis warned, saying he expects damage across the state.
He also warned people to prepare for power cuts.
"Even if the eye of the storm doesn't hit your region, you're going to have really significant winds, it's going to knock over trees, it's going to cause interruptions," DeSantis said, adding that flooding is likely.
The governor urged residents to stock up on food, water, medicine and fuel, and he called up 7,000 National Guard members to help with the effort.
NASA said it was rolling back its massive Moon rocket into its storage hangar at the Kennedy Space Center in Florida because of the hurricane.