Winds of up to 150mph (240km/h) tore off roofs, uprooted trees and downed power lines in Jamaica as the storm's centre passed just south of the island.
Experts say Dean could get stronger still. It is expected to hit Mexico's Yucatan Peninsula late on Monday.
But authorities in the Cayman Islands said the territory had been spared the brunt of the hurricane.
A hurricane warning is in effect for the coast of Belize and the east coast of the Yucatan Peninsula, from Belize City north to Cancun.
Although the Cayman Islands were bracing themselves for severe winds, the hurricane's eye passed 100 miles (160km) south of the islands. The strongest gusts measured just 57mph (92kph).
Daniel Brown, from the US National Hurricane Center (NHC), said the focus was now on other areas. 
Enlarge Map"It looks like the biggest threat is going to be for portions of northern Belize and the Yucatan Peninsula coast of Mexico," he said.
At 0800 EDT (1200 GMT) the storm was about 440 miles (710km) east of Belize City, in Belize, which borders Mexico, and moving at nearly 21mph (33km/h).
The hurricane is heading west and is expected to move slightly north-westwards across the Yucatan Peninsula, the NHC said.
After crossing the Yucatan, the storm is forecast to move over the Bay of Campeche in the south-west Gulf of Mexico, before striking Mexico's coast again near Tampico.
'A good beating'
The NHC said Dean, already "extremely dangerous", may reach Category Five strength within the next 24 hours, with sustained winds greater than 155mph (249km/h) and a storm surge 18ft (5.5m) above normal tide levels.
We are all boarded up sitting in the front room listening to the local radio and drinking wine 
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George Town, Grand Cayman
Dean: Where next? In Cancun and other resorts on the Yucatan, windows have been boarded up and thousands of tourists have been moved out or turned away.
The resort's airport was packed with tourists trying to get away while the normally busy areas were virtually empty.
Workers have also been evacuated from oil rigs in the Gulf of Mexico and officials in southern Texas have urged residents to leave the area.
Dean has already claimed at least six lives in the eastern Caribbean.
The eye of the storm was some miles out to sea as it passed by Jamaica, but it still caused widespread damage as it careered along the south coast.
"I took a journey onto the streets of Kingston and saw huge trees, massive mango trees, coconut trees that have blocked the roads," said Kathy Barrett from Radio Jamaica.
"Power lines are down, it really has been - we got a good beating from Hurricane Dean."
Prime Minister Portia Simpson Miller declared a month-long state of emergency, widening the powers of security forces.
A general election is due to take place on 27 August, but the storm has cast doubt on that date.
Shuttle re-scheduled
When the hurricane passed through eastern parts of the Caribbean at the weekend rough waves damaged buildings on the coast of the Dominican Republic and thousands of people were left without electricity and took refuge in schools and churches on the Haitian island of Gonave.
Six deaths have been confirmed as a result of Dean:
- A boy was swept out to sea and drowned in the Dominican Republic's capital, Santo Domingo
- In Martinique, a woman in her early 80s died of a suspected heart attack during the hurricane's passage while a man died after sustaining a fall
- In Dominica, a landslide crushed a woman and her seven-year-old son while they slept in their home
- A man aged 62 was swept away and drowned in St Lucia when he tried to retrieve a cow from a rain-swollen river
In the US, the return of the space shuttle Endeavour was brought forward by a day, to Tuesday in an attempt to beat the hurricane should it eventually reach Texas, where Nasa's mission control is based.
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