"It's arrived, with all its diabolical force," Cuban leader Fidel Castro said of the hurricane during an appearance on state television on Friday afternoon.
He said there were 10 deaths in southeastern Cuba.
Another 22 people earlier were reported killed in Haiti, bringing the known overall death toll for the Caribbean to 32.
"It is a very strong Category Four, almost a Category Five", the strongest level on the Saffir-Simpson scale, Cuban Meteorological Institute chief Jose Rubiera said after Dennis made landfall around 1700 GMT near the central province of Cienfuegos.
Cuban authorities rushed more than 700,000 people into shelters between late Thursday and Friday including at least 2500 foreign tourists.
But at least three provinces sustained serious material damage, a government source said privately. Some 20 homes were destroyed and power was knocked out in Santiago de Cuba, the country's second city on its east end.
Communications towers were toppled and tourist facilities in Santiago province sustained serious damage, the source added.
Forecasters warned Dennis could pass dangerously close to Key West in Florida early on Saturday on its way to the Gulf of Mexico where 116 oil platforms and rigs have been evacuated.
In Haiti, at least 20 were injured and 30 remain missing in addition to those killed.
Most of the victims were in the south and southeast of Haiti where heavy rains caused flooding of cities and destruction of crops in the countryside, according to Jeffe Delorges, a civil protection spokesman. Some 8000 people were displaced.
Thousands of residents evacuated Key West, Florida's southernmost city, as well as areas along the US Gulf coast.