Rafael hit western Cuba on Wednesday as a major Category 3 hurricane and swept across the island in two and a half hours before losing intensity as it entered the Gulf of Mexico.
It came just two weeks after Hurricane Oscar, which left eight dead in the east of the island during a national electricity blackout that lasted four days.
President Miguel Diaz-Canel said that the provinces of Artemisa, Havana and Mayabeque were worst hit.
Writing on the social platform X, he said that authorities were working to restore power to the center and east of the island and were assessing the damage to infrastructure in the west "to start recovery (of power) there too."
In Havana, residents used brooms, shovels and buckets to clear branches, garbage, mud and pieces of cement from the streets.
The highway from the capital west to Artemisa was dotted with fallen electricity pylons and the streets of towns along the route were strewn with branches, tiles and pieces of concrete from damaged homes.
In the town of Candelaria, around 40 km from where Rafael made landfall, 49-year-old housewife Lidia was in despair.
"Now, the hurricane is leaving and we have another blackout, meaning we won't have water," she said standing outside her house. "What are we going to cook? What water are we going to drink?"
Cuba has been suffering hours-long power cuts for months -- a symbol of the island's worst economic crisis since the fall of the Soviet Union, a key ally and financial backer, in the early 1990s.
The UN General Assembly last week renewed its long-standing call for the US to lift its six-decade trade embargo on the communist island.
