The Category 4 storm has already claimed six lives in the Dominican Republic and Martinique.
It is due to hit Jamaica at around midday with 155mph (249kph) winds and bring up to 20 inches (50cms) of rain.
The Jamaican authorities have been moving people into more than 1,000 shelters nationwide.
Residents jammed supermarkets and hardware stores in the capital Kingston to stock up on canned food, bottled water and torches.
The hurricane is expected to reach the low-lying Cayman Islands on Monday.
According to the Federation of Tour Operators, there are currently just under 4,000 Britons on holiday in Jamaica and a "handful" on the Cayman Islands.
Authorities on Martinique confirmed two deaths, including a woman who drowned in her home.
In St Lucia, a 62-year-old man drowned in a river swollen by rain.
A woman and her seven-year-old son died in Dominica when a hillside gave way and crushed their house.
Reports said a boy was also dragged into the sea and drowned while watching waves on the Dominican Republic coast.
Dean is on course to clip Mexico's Yucatan Peninsula and enter the Gulf of Mexico by Tuesday.
Forecasters said it was too soon to say whether it will strike the United States.
NASA has ordered the space shuttle Endeavour to return to Earth on Tuesday - a day early - in case the storm threatens Houston, Texas, where Mission Control is based.
Waiting For The Hurricane
Jamaica is on full alert for the arrival of Hurricane Dean, with residents being moved into more than a thousand shelters across the island. Sky's Sara Merchant reports.
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