The hurricane's eye reached Cuba early Friday afternoon and maximum sustained winds slowed slightly as it moved over island.
The storm's raging winds and intense rains had already caused power outages in most of Cuba as well as heavy flooding, but there were no immediate reports of injuries, the Cienfuegos office of Civil Defence said.
Thousands of people had been evacuated in anticipation of the onslaught of Dennis, a category 4 hurricane in the Saffir-Simpson scale with sustained winds of 240 kilometres per hour.
Cuban officials said the hurricane would affect at least 12 provinces as it swept through the island and continue on its way to Florida.
Dennis was expected to hit U.S. shores as a "major hurricane'' this weekend or early Monday. A four is the second highest category in measuring the strength of a hurricane.
A hurricane warning is already in effect for parts of the Florida Keys, the National Hurricane Centre in Miami said, and Florida Governor has issued a state of emergency.
In a press conference, Florida Governor Jeb Bush asked citizens to be ready for mandatory evacuations.
Cuba ordered a "cyclone alert'' throughout the country and 200,000 people were evacuated to safe zones, including several thousand tourists. All schools were closed and aviation authorities grounded planes on national flights.
Dennis, which could bring up to 40 centimetres of rain with it, has already killed five people and caused flooding in Haiti. The storm sparked flooding also in Jamaica.
The National Hurricane Centre has warned that Dennis could cause "life-threatening'' floods and landslides, as well as large waves.
Hurricane and tropical storm warnings have been issued for all of southern Florida along the state's Gulf Coast, and authorities ordered all non-residents to leave the Florida Keys. The U.S. state was wracked by four hurricanes last year.
Dennis, the first of four tropical storms so far this season to have reached hurricane strength, was on a similar route as that followed last year by Hurricane Ivan, a category five hurricane that left 65 dead in the Caribbean, 31 dead in the United States and a swathe of destruction. The region is still recovering from that storm.
Last season's whirlwind of successive lethal hurricanes was one of the worst on record, and the region was still not fully back on its feet in the face of new onslaughts.
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- Deutsche Presse Agentur
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