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 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.
The hurricane left hundreds of thousands of people without electricity and swamped fishing villages as it tracked northward toward Florida. No fatalities had been reported as of Tuesday night.
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 braces as Ian is upgraded to Category 4 storm
The US National Hurricane Center said on Wednesday that Ian had strengthened into a Category 4 storm as it bore down on the state of Florida with winds of 140 miles (225 kilometers) per hour.
"Air Force hurricane hunters find Ian has strengthened into an extremely dangerous Category 4 hurricane," the NHC said in an advisory.
As of 05:00 local time (09:00 UTC/GMT), mandatory evacuation orders were issued in a dozen coastal Florida counties, while voluntary evacuations were recommended in a number of areas, according to the state's emergency officials.
Coastal residents emptied grocery shelves, boarded up windows and fled to evacuation shelters as Ian lashed Florida'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.
lo/mkg (AFP, AP, Reuters)