The evacuation of more than a million people comes as the category four storm moves off the north-eastern coast of Cuba towards Florida.
Hurricane Matthew, which has been described as the most powerful Caribbean hurricane in nearly a decade, has already left thousands of people displaced in Haiti.
Reports say the hurricane made landfall with winds of up to two hundred and thirty kilomtres per hour.
It also triggered heavy rainfall and dangerous storm surges that have led to a number of deaths in Haiti and the nearby Dominican Republic.
A bridge linking southern Haiti to the capital, Port-au-Prince has collapsed, as the hurricane moved towards the north-eastern coast of Cuba.
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