The dead person “did not respect orders to stay inside”, authorities said in a statement, adding that “several floods have been signalled” around Pointe-a-Pitre, Guadeloupe’s largest city.
Coastal areas around the capital Basse-Terre have also been “submerged”.
“All of the archipelago’s road networks have been affected by falling trees or branches,” it said.
Little damage to buildings had been reported so far, though “some roofs have been ripped off”.
Authorities said 40 percent of households in the territory of some 400,000 had no electricity, and 25 per cent of landlines had been cut.
The US National Hurricane Center described Maria as “potentially catastrophic” as it pushed northwest towards the Virgin Islands and Puerto Rico.