Irma was projected to hit the Leeward Islands, causing storm surges, life-threatening winds and torrential rain.
The US state of Florida has declared a state of emergency.
It comes as residents in Texas and Louisiana are reeling from the effects of Hurricane Harvey, which struck as a category four storm, causing heavy rain and destroying thousands of homes.
However the NHC warned that it was too early to forecast Irma's exact path or effects on the continental US.
Irma was set to reach the Leeward Islands, east of Puerto Rico, by late Tuesday or early Wednesday (local time), the centre added. The storm was moving at a speed of 20km/h (13mph).
It may cause rainfall of up to 25cm (10in) in some northern areas and raise water levels by up to 3m (9ft) above normal levels, the NHC said.
Puerto Rico also declared a state of emergency and activated the National Guard. Governor Ricardo Rossello announced the opening of emergency shelters able to house up to 62,000 people, and schools would be closed on Tuesday.
Long queues of people formed in shops, with residents stocking water, food, batteries, generators and other supplies.
Hurricane warnings have been issued for the islands of Antigua and Barbuda, Anguilla, Montserrat, St Kitts and Nevis, St Martin, Sint Maarten, St Barthelemy, Saba, St Eustatius, Puerto Rico, British Virgin Islands and US Virgin Islands. It means that hurricane conditions are expected in the next 36 hours.
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