A family of four drowned after their basement flat in Arzachena town, some 300 km from the autonomous island's capital Cagliari, was filled with water.
Three people were killed when a bridge collapsed on their car near Olbia city, around 280 km from Cagliari, media reports said.
Prime Minister Enrico Letta has declared a state of emergency.
A mother and her daughter were found dead in a car after it was swept away by a flash flood, while a police officer died when a bridge collapsed during a rescue effort. A number of people are also reported missing across the Mediterranean island.
Declaring a state of emergency Prime Minister Letta announced that 20 million euros would be allocated immediately to relief efforts.
Hundreds of people have evacuated their homes due to the flooding caused by Cyclone Cleopatra. Media reports say flood waters in some areas were up to three metre high. The storm has caused extensive damage to farms and properties. Further bad weather is expected in the coming days.