The hurricane is packing winds of 230 km per hour, according to the US National Hurricane Centre.
The NHC said the storm was expected to strengthen before passing over Jamaica towards the Gulf of Mexico.
It said in a statement: "Dean could become a potentially catastrophic category five hurricane at any time before it reaches Yukatan [Mexico's Yucatan Peninsula]."
The area is home to a third of US domestic crude-oil production and 15 per cent of its natural gas production.
The storm has also affected the mission schedule for Endeavour, the US space shuttle.
Nasa, the US space agency, has brought forward the landing for the shuttle by a day, in order to guarantee a safe landing should the hurricane reach Texas, home to Nasa's mission control.
Jamaica has gone on full alert as it prepares for the storm to pass.
Several airports have been closed and thousands of people went to markets and petrol stations to stock up on essentials.
Portia Simpson Miller, the Jamaican prime minister, said the country was confronting a national emergency and urged people in flood-prone areas to seek shelter.
"Do not wait for the last minute to make the decision to move from where you are," Miller said.
"Decide now and begin to make arrangements to leave now."
Thousands of tourists filled airports for flights out of the region.
Garfield Buford, a journalist on the island, told Al Jazeera that Jamaicans were on full alert, despite reports that the island may escape the full brunt of the storm.
"The latest we are hearing is that the eye of the hurricane may not make land but it is expected to continue along the south coast of the island," he said.
"Jamaicans are not taking any chances."
Authorities in eastern Cuba also began evacuating tens of thousands of people to save them from possible flooding and destruction as Dean passes.
Civil defence authorities said 35,000 people were under the evacuation order in the southeastern province of Holguin.
Mexico's government also declared a state of emergency as Dean headed toward its southern Gulf of Mexico oilfields and the refining center of Tampico.
Quintana Roo state Governor Felix Gonzalez ordered the evacuation of 80,000 tourists from Cancun and other popular barrier islands.
"We can evacuate 30,000 tourists by air every day. That gives us enough time to leave hotel occupancy at a minimum, with a reasonable number of guests we can assist and put up in shelters," he said.
The storm is the first hurricane of the Atlantic season, and has already rolled through the Caribbean to the south of Hispaniola, the island shared by Haiti and the Dominican Republic.
Heavy rain and rising seas had caused flooding on Saturday in coastal areas of the island.
Samuel Menager, an employee at World Vision, an international aid group that helped evacuate people, said that in Gonave, an island west of Port-au-Prince, electricity was cut off as thousands of people gathered in the darkness in churches, schools and other inland shelters as the storm brought heavy rain and fierce winds.
Eladio Martinez, the governor of eastern Santo Domingo province, had said on radio that a 16-year-old boy was reported dead and several injured in the Dominican Republic.
Emergency officials have also said that at least five houses were destroyed and 15 others were heavily damaged along the Dominican coast.