Strong winds and heavy rains are already lashing the islands, east of Puerto Rico in the northern Caribbean.
A new hurricane warning has now been issued for the Puerto Rican islands of Culebra and Vieques, said the US-based National Hurricane Center (NHC).
Hurricane warnings are already in effect in Anguilla, St Martin and St Barthelemy, St Maarten, Saba, St Eustatius, the British Virgin Islands and the US Virgin Islands.
Hurricane warnings are in place for Antigua, Barbuda, Montserrat, St Kitts, Nevis, Anguilla, Saint Martin, Saint Barthelemy, St Maarten, Saba, St Eustatius, the British Virgin Islands and the US Virgin Islands. Puerto Rico is also on hurricane alert.
The hurricane warning for Antigua, Barbuda, Montserrat, St Kitts and Nevis has been downgraded to a tropical storm warning. The Turks and Caicos islands are on alert.
People in the area are making preparations ahead of the storm, stocking up on food, water and other essential supplies, as well as trying to protect property.