Almost 150 millimetres (six inches) of rain fell, overloading the drainage system, the municipality said in a statement, describing it as an "event of exceptional magnitude".
The heavy rain caused mudslides and vehicles parked close to waterways were dragged downstream by what became fast-running rivers.
Firefighters carried out more than 100 operations, including using inflatable boats to rescue people trapped in their homes.
Thanks to a weather warning, no injuries were reported in the affected areas, the civil protection agency said.
Bad weather also hit the region of Calabria, across the Strait of Messina on the Italian mainland, causing Catanzaro mayor Nicola Fiorita to urge fellow residents to stay at home.
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