The new storm, which the US National Hurricane Center (NHC) warned could become a "major hurricane", threatens the French territory of Guadeloupe, the staging area for relief operations for several islands hit by Irma.
Guadeloupe was going on "red alert" Monday with schools, businesses and government offices ordered closed, as was neighbouring Martinique. Each has a population of around 400,000 people.
The hurricane is expected to hit at around midday local time.
Warnings were also triggered for Dominica, St Kitts and Nevis and the British island of Montserrat.
French Interior Minister Gerard Collomb warned in Paris on Sunday that "we will have major difficulties" if Guadeloupe is hard hit, noting that the territory was "the logistical centre from where we could supply St Martin and organise all the airlifts."
Irma killed 15 people on St Martin, an island shared by France and the Netherlands.
Officials in Guadeloupe predicted severe flooding in low-lying areas and urged residents to move to higher ground.
France, Britain and the Netherlands have been criticised for the pace of relief efforts and for struggling to contain lawlessness in their overseas territories amid widespread shortages of food, water and electricity after Irma.
'Culture Of Risk'
But in Guadeloupe's capital Pointe-a-Pitre, local official Josette Borel-Lincertin said authorities had ample experience of preparing for hurricanes.
"We have a culture of risk, we know what needs to be done," she said.
Collomb said an additional 110 soldiers would be deployed to the region to reinforce about 3,000 people already at work tackling security problems, rebuilding infrastructure and supplying food and water to hurricane-hit islanders.
He said up to 500 more people could be sent if needed.
Irma, a Category Five hurricane, left around 40 people dead in the Caribbean before churning west and pounding Florida, where at least 20 people were killed.
As of 0600 GMT, Maria was a Category One hurricane, the lowest on the five-point Saffir-Simpson scale, with maximum sustained winds of 90 miles per hour (150 kph).
As of 0900 GMT the storm was about 160 kilometres (100 miles) east of Martinique and moving at 13 mph, the NHC said.
Tropical storm warnings were in place in Antigua and Barbuda, Saba and St Eustatius, and St Lucia. The tiny island of Barbuda was decimated by Hurricane Irma on September 5-6 when it made its first landfall in the Caribbean as a top-intensity Category Five storm.
The NHC said Maria could produce a "dangerous storm surge accompanied by large and destructive waves" that would raise water levels by four to six feet (1.2 to 1.8 metres) when it passes through the eastern Caribbean.
It also forecast a maximum potential rainfall of 20 inches (51 centimetres) in the Leeward Islands, Puerto Rico and the US and British Virgin Islands through Wednesday night -- conditions that could cause life-threatening flash floods and mudslides.
A second hurricane, Jose, is also active in the Atlantic and has triggered tropical storm watches for the northeastern United States.
Irma broke weather records when it sustained winds of 295 kilometres per hour (183 miles per hour) for more than 33 hours.
Many scientists are convinced that megastorms such as Irma, and Harvey before it, are intensified by the greater energy they can draw from oceans that are warming as a result of global climate change.
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