Irma, now a category three hurricane with maximum sustained winds of 120 mph (195 kph), should continue strengthening through Tuesday, the NHC said in an advisory issued at 1500 GMT.
Some forecasters expect it to reach category four strength -- the maximum attained by Hurricane Harvey, which recently devastated parts of Texas and Louisiana -- by that time.
Irma is projected to reach the Leeward Islands, east of Puerto Rico, by late Tuesday or early Wednesday, bringing water levels up to 9 feet (3 meters) above normal levels, rainfall of up to 10 inches (25 centimeters) in areas, and "large and destructive waves."
Irma's path remains unclear, but several projections have it passing over Haiti, the Dominican Republic and Cuba before turning north toward Florida and then possibly swinging up the US East Coast.
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For now, hurricane warnings have been issued for the islands of Antigua, Barbuda, Anguilla, Montserrat, St. Kitts and Nevis, St. Martin, Sint Maarten, St. Barthelemy, Saba and St. Eustatius. A warning means hurricane conditions are expected in the next 36 hours.
Hurricane watches -- meaning hurricane conditions are possible within 48 hours -- have been issued for some of the more populous parts of the Caribbean, including Puerto Rico, Guadeloupe and the US and British Virgin Islands.
Island residents have been advised to monitor the developing storm. On the French island of Guadeloupe, people have been stocking up on provisions, leaving some store shelves empty.
Schools on Saint Barthelemy and Saint Martin have delayed their reopening after summer vacation. Authorities on some islands were alerting residents to the location of storm shelters.