Raging floodwaters swept two children aged three and seven to their deaths in the Delmas district of the capital, and a 24-year-old woman was killed when a church wall collapsed on her house.
Three more people died in the western, coastal Carrefour district of the city.
Haiti, the poorest country in the western hemisphere, is prey to torrential Caribbean storms and Port-au-Prince's garbage-choked drainage channels struggle with the worst downpours.
Some citizens are still living rough or in substandard housing five years after a devastating earthquakes killed more than 200,000 people and levelled entire neighborhoods.
The head of civil protection in the capital region, Nadia Lochard, said that more than 8,000 homes had been flooded in the latest rains, mostly in the Cite Soleil slum and Tabarre suburb.
Officials said the weather forecast looks less menacing for the remainder of the week, but Haiti's annual rainy season normally begins in April and more storms are expected.