Tropical storm Alberto has brought heavy rains to Cuba, dropping as much as 20 inches (50cm) on western areas of the country.
Alberto is not expected to develop into a hurricane
State TV showed pictures of extensive flooding, with one resident of Juventud island saying he had not seen water levels so high in 30 years.
Alberto is the first named storm of the Atlantic hurricane season.
It is expected to veer towards Florida in the next few days, but is considered unlikely to strengthen significantly.
Last year's record-breaking hurricane season saw the region lashed by 28 storms, 15 of which went on to become hurricanes.
The US National Oceanic and Atmospheric Administration (Noaa) has warned that activity this season will also be above normal, though it is not expected to reach last year's devastating heights.
Alberto formed off the western coast of Cuba
The US National Hurricane Center said it had maximum winds of 45 mph (70km/h). It warned the storm could dump up to 30 inches of rain on western Cuba, triggering possible life-endangering flash floods and mudslides.
The BBC's Stephen Gibbs in Cuba said TV pictures suggest the Juventud island is worst affected, with most streets flooded.
Exceptionally heavy rain has also been falling in tobacco-growing areas of western Cuba.
Workers have been doing what they can to protect the crop, particularly those leaves which are being stored in vulnerable drying out sheds, he says.
Noaa predicts that Alberto, currently centred in the Gulf of Mexico north-west of Cuba, will turn north or north-west across Florida.
It warned Florida to expect rainfall of four to eight inches on Monday.
The US hurricane season started on 1 June and lasts until 30 November.
The US Climate Agency has predicted between 13 and 16 named storms this season, of which four are predicted to be "major storms" of category three or above.