The eye of the storm made its second landfall in Cuba's Pinar del Rio province, about 55 miles (90km) south-west of Havana, packing sustained winds of 80mph (130km/h).
Ike first struck in Holguin province, which is home to the nickel mines, the country's top export earner.
The BBC's Michael Voss in Havana says it is still too early to tell the full extent of the economic impact wrought by Ike.
Tens of thousands of buildings have been damaged and crops destroyed.
There is also likely to be an impact on the tourist industry, our correspondent says.
As the storm heads out into the Gulf of Mexico, it is expected to pick up speed and is projected to reach the US Gulf coast.
Louisiana's governor has warned coastal residents to be prepared to move inland.
However, the US National Hurricane Center said it was still too early to tell in which direction Ike would move.
The United Nations cultural agency, Unesco, has offered to help the Cuban government make good any damage to heritage sites and important buildings in Havana.
The agency's director in Havana, Herman van Hooff, said that the latest storm could be a setback to restoration work.
"Since the [1990s] there has been a very strong management system in place for the old Havana area, and a lot has been restored since then," he told the BBC.
"There is still a lot of fabric, a lot of architecture, a lot of housing that is in a fragile state, so any impact by a hurricane, be it wind or rain, is a great concern to everybody."
Cuba is still reeling from the effects of Hurricane Gustav, which hit just over a week ago, damaging almost 100,000 homes in the west of the island.
Ike earlier caused 66 deaths in Haiti and reportedly damaged 80% of the homes in the Turks and Caicos Islands.
Haiti, the poorest country in the Western hemisphere, has endured the onslaught of four tropical storms in a three-week period, causing more than 550 deaths.