Maria is now a Category 5 hurricane, the National Hurricane Center said.
It is due to hit the Leeward Islands, with the eye passing directly over Dominica in the coming hours.
Maria is moving roughly along the same path as Irma, the hurricane that devastated the region this month.
Martinique declared a maximum-level alert while another French island, Guadeloupe, ordered evacuations.
Hurricane warnings are also in place for:
- Dominica: A former British colony with a population of 72,000 about half way between Guadeloupe and Martinique. The eye of the hurricane was about 45 miles (72km) east-south-east at 21:00 GMT on Monday and expected to pass close by
- Puerto Rico: The US territory expects Maria to make landfall as a category three on Tuesday. It escaped the worst of Irma and has been an important hub for getting relief to islands more badly affected. Governor Ricardo Rossello urged islanders to seek refuge
- US Virgin Islands and British Virgin Islands: Both island chains suffered severe damage from Irma and President Donald Trump declared a state of emergency for the US territories on Monday. British authorities fear debris left behind by Irma could be whipped up by the new storm and pose an extra threat.
Warnings are also in effect for St Kitts and Nevis, Montserrat and St Lucia while hurricane watches are in place for St Martin, Saba, St Eustatius and Anguilla.
Some of these islands are still recovering after being hit by Hurricane Irma – a category five hurricane which left at least 37 people dead and caused billions of dollars’ worth of damage.
The Leeward Islands, where Maria will first strike, include Antigua and Barbuda. The latter island was evacuated after being devastated by Irma.
The US National Hurricane Center (NHC) has warned that heavy rainfall caused by the hurricane “could cause life-threatening flash floods and mudslides”.