According to the US National Hurricane Center, the storm is expected to hit Haiti and Jamaica on October 3.
Residents have been frantically stocking up on emergency supplies.
Jamaica’s PM Andrew Holness has urged citizens to make all preparations before it is too late.
However, he told Reuters that Jamaica was prepared for the category 4 hurricane.
In Jamaica, the powerful storm is expected to bring up to 25 inches of rain, which could trigger life-threatening landslides and floods, according to forecasters.
In the capital Kingston, supermarkets were crowded with people looking for canned foods, water and flashlights.
Officials have warned the high winds could batter the country’s main tourist areas including Montego Bay in the north.
In Haiti, the poorest country in the Americas, residents from outlying islands have been evacuated, and officials have banned boating.
The hurricane is expected to cause up to 40 inches of rain in Haiti.
Hurricane Matthew is expected to hit Cuba on October 4, potentially hitting the colonial city of Santiago de Cuba and the US Navy base of Guantanamo Bay.
A mandatory evacuation of non-essential personnel, including about 700 family members of military personnel, was underway at the base and everyone remaining there was being told to take shelter, the Navy said in a statement.
There are about 5,500 people living on the base, including 61 men held at the detention centre.
Cuban President Raul Castro traveled to Santiago to supervise preparations.
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