As Irma left Cuba late on Saturday and directed its 200kmh winds towards Florida, authorities on the island were assessing the damage.
They warned of staggering damage to keys off the northern coast studded with all-inclusive resorts and cities, as well as farmland in central Cuba.
There were no immediate reports of deaths in Cuba - a country that prides itself on its disaster preparedness - but authorities were trying to restore power, clear roads and warning that people should stay off the streets of Havana because flooding could continue into Monday.
Residents of "the capital should know that the flooding is going to last more than 36 hours, in other words, it is going to persist," Colonel Luis Angel Macareno said late on Saturday, adding that the waters had reached about 600 meters into Havana.
As Irma rolled in, Cuban soldiers went through coastal towns to force residents to evacuate, taking people to shelters at government buildings and schools - and even caves.
Video images from northern and eastern Cuba showed uprooted utility poles and signs, many downed trees and extensive damage to roofs.
Witnesses said a provincial museum near the eye of the storm was in ruins.
And authorities in the city of Santa Clara said 39 buildings collapsed.
More than 5,000 tourists were evacuated from the keys off Cuba's north-central coast, where the government has built dozens of resorts in recent years.
Civil defence official Gregorio Torres said authorities were trying to tally the extent of the damage in eastern Cuba, home to hundreds of rural communities and farmland.