Ike earlier caused 61 deaths in Haiti and reportedly damaged 80% of the homes in the Turks and Caicos Islands.
The hurricane first came ashore in Cuba on Monday near Punta Lucrecia in the state of Holguin, about 510 miles (825km) south-east of Havana.
State television broadcast pictures of the accompanying storm surge washing over coastal defences and sending waves crashing into buildings.
Sustained winds of about 160km/h (100mph) tore the roofs off many buildings, knocked down trees and destroyed crops.
One person was killed by a falling tree, an elderly woman died when her house collapsed and two others were electrocuted.
As Ike moved back out to sea, the US National Hurricane Center downgraded it to a Category One hurricane after its maximum sustained winds dropped to about 130km/h (80mph).
However, it said a slight increase in intensity was possible if the storm's centre remained over water.
The eye of the storm is forecast to continue westward along Cuba's southern coast before hitting western Cuba on Tuesday morning and emerging into the south-eastern Gulf of Mexico by Tuesday night.
The Cuban authorities have put the entire population on maximum alert and hundreds of thousands of people have been evacuated to shelters or moved to higher ground.
With Hurricane Gustav striking just a week ago, Cuba's internationally acclaimed emergency services have been stretched to the limit, the BBC's Michael Voss in Havana says.
Gustav caused serious damage to the western side of the island, damaging almost 100,000 homes.
"In all of Cuba's history, we have never had two hurricanes this close together," said Jose Rubiera, head of Cuba's meteorological service.
A direct hit on Havana, a densely populated city of two million people, with crumbling colonial buildings, could be devastating.
The capital has been put on alert as authorities prepared to evacuate residents from some of the older buildings.
The United Nations cultural agency, Unesco, has offered to help the Cuban government make good any damage to heritage sites and important buildings.
The agency's director in Havana, Herman van Hooff, said that the latest storm could be a setback to restoration work.