The Communist Party daily newspaper Granma listed the victims, who ranged in age from 18 to 75, but provided no specific causes of death.
A sudden, two-hour downpour late Tuesday dumped 120 millimeters (nearly 5 inches) of rain in the capital. Areas near the city's rivers were most affected, Granma said.
Water cisterns at hospitals and offices citywide were contaminated, and electricity affected in several parts of town, the newspaper reported. Traffic tunnels were flooded and shut down, the AP reports.
The rains have also suspended Cuba's national championship baseball series. Game three of the baseball championship between the Havana team Industriales and Santiago de Cuba was rained out Tuesday, then suspended Wednesday night as well.
The teams are tied after two games in the best-of-seven series.