Gusts of wind up to 200 kilometres per hour (125mph) were recorded in the capital Havana, as the island faced its most powerful hurricane for more than 50 years.
The storm has now weakened as it blew on to the Bahamas, and the authorities in Nassau reported no major damage apart from flooding and the loss of power.
The storm also threatened but ultimately did little damage to south Florida and the Keys and storm warnings were dropped for the state's Atlantic coast.
Darkness
The Cuban authorities are assessing the damage caused by winds and rain that caused led to the evacuation of at least 700,000 people from low-lying areas.
Tourists have been taken from resorts to hotels in the capital, and student camps on the southern Zapata peninsula have been evacuated.
All national and international flights have been cancelled and public transport suspended.
Electricity in the capital has been cut off to avoid accidents with falling power cables.
"The whole of Havana is in total darkness, everyone is using candles," one resident said.
Reports say that large areas of agricultural land, especially in the west and centre of the country, have been devastated and homes have been damaged.
Heavy damage to Cuba's sugar, banana, citrus and coffee crops is expected.
There is also severe flooding, mostly in coastal areas. The state television, running on emergency generators, spoke of medical workers wading knee-deep through sea water in Havana's main hospital.
Central America damage
Earlier, Hurricane Michelle led to the deaths of at least 12 people in Central America, as heavy rains flooded rivers and caused mudslides.
Thousands of residents of the Atlantic coasts of Honduras and Nicaragua have been left homeless.
Ten people were confirmed dead in Honduras, where some coastal areas received half their usual annual rainfall in five days last week.
Atlantic coast residents were reportedly trapped for days on rooftops or patches of high ground, and some were said to be surviving on the carcasses of drowned farm animals.
In Nicaragua, officials say some 10,000 people have been made homeless by the hurricane.
The two countries are still struggling to recover from the devastation caused by Hurricane Mitch in 1998, when some 20,000 people were killed in the region, and more than six billion dollars' worth of damage was caused.