Tropical storm Imelda was expected to continue its path across the northwest Bahamas and eastern Cuba through Tuesday.
State media in Cuba reported that 60-year-old Luis Mario Pérez Coiterio died in Santiago de Cuba following landslides in that area.
Overfilled rivers caused a bridge to collapse, leaving some municipalities isolated. Overall,
Imelda forced the evacuation of some 1,291 people across Cuba, with 158 of them staying in shelters.
Authorities in the Bahamas have closed a majority of schools following mandatory evacuations for some islands in the archipelago as Tropical Storm Imelda drops heavy rain and unleashes flooding in parts of the northwestern Bahamas, including Eleuthera, the Abacos, Grand Bahama Island and the surrounding keys.
Heavy rains also were forecast along the coastline of North and South Carolina.
The Tropical Storm had maximum sustained winds of 60 mph (95 kph) and was moving north at 9 mph (15 kph).
It was forecast to become a hurricane on Tuesday and spin out to open ocean, according to the National Hurricane Center in Miami.
Meanwhile, Hurricane Humberto, a Category 4 storm, churned in open waters nearby, which forecasters said would cause Imelda to abruptly turn to the east-northeast, away from the southeastern United States coast.