Authorities in the US state of Florida called off evacuation plans after the hurricane appeared likely to miss the Florida Keys islands.
The US National Hurricane Centre also warned that Ike could strengthen again as it headed toward the Gulf of Mexico.
Ike had swept ashore in northeastern Cuba late on Sunday near Punta Lucrecia, about 820km southeast of Havana, the capital.
Cuba's state-run television showed images of huge waves slamming into sea walls in the city of Baracoa, flooded streets, toppled trees and damaged buildings.
Cuban weather forecasters said Ike would pass near or over Havana as it leaves the island on Tuesday.
Authorities have begun evacuating tens of thousands of residents from crumbling apartment buildings and low-lying parts of the city.
"Attention Havana, attention Havana. Havana is on hurricane alert. All residents must strictly follow the instructions of the civil defence," local radio stations broadcast.
Officials said at least 1.5 million people had been evacuated from vulnerable areas in Cuba, which is also recovering from Gustav's strike last week on western provinces.
Ike, a category three storm, had earlier ripped through the southern Bahamas and the Turks and Caicos islands, as well as Haiti.
Officials said at least 47 people - 13 of them children - had died recently from the floods in Haiti, in addition to the 500 killed last week by Tropical Storm Hanna.
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.