Maria is approaching the eastern Caribbean less than two weeks after Irma hammered the region before overrunning Florida.
That storm, one of the most powerful ever recorded in the Atlantic with winds up to 298km/h, killed at least 84 people, more than half of them in the Caribbean.
Hurricane conditions were expected for nearby Guadalupe, Dominica, Martinique and St. Kitts, Nevis and Montserrat, and the hurricane centre is warning residents of Puerto Rico to monitor the storm.
The British Virgin Islands and St. Martin, which was devastated by Hurricane Irma, were under a hurricane watch, as were the US Virgin Islands and Anguilla.
More than 1,700 residents of Barbuda, where Irma damaged nearly every building, braced for Maria on Antigua, now under a tropical storm watch, said Ronald Sanders, the country's ambassador to the United States.
Puerto Rico has already begun preparations for Maria, which by Tuesday was expected to unleash powerful winds on the US territory, already dealing with a weakened economy and fragile power grid.
Damage to Puerto Rico could also disrupt the disaster relief supply chain to other islands that were hit by Irma.
Puerto Rico Governor Ricardo Rossello said officials had prepared about 450 shelters with a capacity for nearly 68,000 people - or even 125,000 in an emergency. He said schools were cancelled for Monday and government employees would work only a half day.
Officials in the Dominican Republic urged people to leave areas prone to flooding and said fishermen should remain in port.
A tropical storm watch has also been issued for portions of the US mid-Atlantic and New England coast with a second hurricane, Jose, moving slowly north from its position in the Atlantic Ocean about 510km southeast of Cape Hatteras, North Carolina.
The eye of Jose, with top sustained winds of 150km/h, should remain off the US East Coast, the NHC said.