The category five hurricane began lashing St Croix in its north-westerly path across the Caribbean.
On Monday it inflicted substantial damage on Dominica and the first aerial images of the island have emerged.
The storm is moving roughly along the same track as Irma, this season's other category five hurricane.
The governor of Puerto Rico, a US territory, has told the island's 3.5 million people to seek shelter with the hurricane poised to make landfall around 8am local time (1300 GMT).
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Officials there fear the debris left by Irma earlier this month could now prove extremely dangerous in the winds of Maria.
There are also concerns that heavy rain could cause landslides in some places, and that a predicted storm surge of up to 9 feet (2.7m) could swamp low-lying areas.
Puerto Rico has been a haven for people fleeing other storm-ravaged Caribbean islands in recent weeks.
Hundreds of shelters have been set up by the authorities.
What do we know of the damage on Dominica?
The first aerial footage of the island confirms "significant damage", Ronald Jackson of the Caribbean Disaster Emergency Management Agency says.
It shows flattened buildings, rivers which have burst their banks and a flooded runway.
Dominica has been virtually cut off with telecommunications severed, but local amateur radio operators say more than 90% of properties have been damaged.
The former British colony, which has a population of 72,000 and is less than 50km long and 25km wide, escaped the worst of Hurricane Irma two weeks ago.
But on Monday the eye of the new category five storm passed directly over.
The last communication from the island was from Prime Minister Roosevelt Skerrit just as the storm struck late on Monday, when he said in a Facebook post that the winds had swept away the roofs of "almost every person I have spoken to or otherwise made contact with."
Where else has Maria passed?
The French territory of Martinique has been hit by power cuts but is thought to have escaped serious damage
Images show flooding in the French territory of Guadeloupe, where one person was killed by a falling tree. At least two others were missing after their ship sank near Desirade, the easternmost island in the archipelago.
Officials described weather conditions as "very bad" with violent winds. About 80,000 homes were without power there, a government statement said.
There are reports of flooding, mudslides and power outages in parts of St Lucia.
Where next?
A storm surge - rising seawater coming in from the coast - is expected to bring "life-threatening" swells of up to 9ft (2.7m) above ground in the US and British Virgin Islands and Puerto Rico, National Hurricane Center forecasters in the US said.
Heavy rainfall of around 25in (63cm) was expected near Puerto Rico and up to 20in in the US and British Virgin Islands.
Puerto Rico's public safety commissioner, Hector Pesquera, issued a stern warning to island residents.
"You have to evacuate. Otherwise, you're going to die," he said. "I don't know how to make this any clearer."
Puerto Rico Governor Ricardo Rossello warned the storm could be "devastating and catastrophic", adding that he expected to lose a lot of infrastructure.
Tropical storm warnings were issued for Antigua and Barbuda, Saba, St Eustatius, St Martin, Anguilla and Martinique.
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How did Maria gather strength so fast?
Maria jumped from a category three to a top-strength category five within just a few hours on Monday, which was a shock for people in Dominica.
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