In its latest update on Monday, the US National Hurricane Center (NHC) said that Maria had maximum sustained winds of 195 km/h (120mph).
The eye of the storm is 100 miles east of Martinique, and Maria is moving west-northwest at about 13mph.
"Preparations to protect life and property should be rushed to completion," the NHC said.
In the French territory of Guadeloupe, schools, businesses and government buildings have all been closed and severe flooding is predicted in low-lying parts of the islands.
Preparations have also begun in Puerto Rico, where Maria is expected to bring strong winds on Tuesday.
The most southerly point of the Leeward Islands - where Maria will first strike - includes Antigua and Barbuda. The latter island was evacuated after being devastated by Irma.
The NHC says that "a dangerous storm surge accompanied by large and destructive waves will raise water levels by as much as 1.5-2.1m (5-7ft) above normal tide levels near where the centre of Maria moves across the Leeward Islands".
It also forecasts a maximum potential rainfall of 51cm (20in) in some areas of the central and southern Leeward Islands - including Puerto Rico and the US and British Virgin Islands - through to Wednesday night.
"Rainfall on all of these islands could cause life-threatening flash floods and mudslides," it warned.