Ike struck Cuba came just one week after hurricane Gustav tore across the Caribbean, hitting Cuba, Haiti, the Dominican Republic and Jamaica and leaving about 80 people dead.
"In all of Cuba's history, we have never had two hurricanes this close together," Jose Rubiera, the head of Cuba's weather service, told the country's state television.
Energy companies in the Gulf of Mexico, which halted oil production during the impact of Gustav, have delayed restarting the flow of oil under the threat posed by Ike.
The weakened hurricane hit Cuba's southwestern coast after at least four people were killed in hurricane-related incidents as Ike roared along the Cuban coastline on Monday.
"There is substantial damage in housing, and we are evaluating the farm sector," said colonel Jose Betancourt, of the Cuban civil defence department.
Cuban authorities also said seven people had also been injured as Ike tore across the country from east to west.
The island had not seen hurricane-related deaths since 16 people were killed in hurricane Dennis in July 2005.
Officials said at least 1.5 million people had been evacuated from vulnerable areas in across Cuba.
Ike had earlier ripped through the southern Bahamas and the Turks and Caicos islands, as well as Haiti.
Officials said at least 66 people, including more than a dozen children, had died from the floods brought by Ike in Haiti, in addition to the 500 killed last week by Tropical Storm Hanna less than a week ago.
Eighty per cent of homes in the Turks and Caicos islands were damaged by winds, although there were no reports of deaths.
Ike has also ripped off roofs and knocked over trees and power lines in the Bahamas' southernmost island of Great Inagua.