The 60-year-old man drowned in the municipality of Jiguani, Granma region after the Bayamo river overflowed its banks, Dunya News reported.
Floods have left several villages cut off, crops destroyed, and power outages.
Granma authorities said more than 7,000 people were evacuated to state-run shelters or family homes, and some 10,000 homes had suffered damage.
The island's Meteorological Institute said the showers and thunderstorms were caused by a combination of a trough in the middle and upper levels of the atmosphere and a flow of humid air from the south.
Weather authorities are forecasting heavy rains for the next 24 hours.
SKH/PR