Rescue services said the holiday villa where they were spending the weekend was suddenly submerged in water and mud.
The victims included children aged one, three and 15. Other family members killed in the disaster were aged between 32 and 65.
They were believed to be spending the weekend at the house in the coastal town of Casteldaccia, east of the Sicilian capital Palermo.
Three people managed to escape, reportedly two children and one adult. Two were out of the house on an errand, and the third survived by climbing a tree and staying there for more than two hours.
“I lost everything, I have nothing left, just my daughter,” the surviving adult, 35-year-old Giuseppe Giordano, told journalists.
His wife, two other children, his parents, brother, and sister, his nephew and the boy's grandmother all died, he said.
Flood survivor Giuseppe Giordano, centre, outside the morgue in Casteldaccia. Photo: AFP/Alessandro Fucarini
Local media reports the house had been built illegally close to the river, which was known to be at risk of flooding.
Death toll continues to rise
Floods have now killed 12 people on the island of Sicily, pushing the storm’s death toll in Italy this week beyond 30, rescuers said.
Several people are also reported missing
After flying over Casteldaccia on Sunday, Sicilian prosecutor Ambrogio Cartosio described scenes of “total disaster”.
Officials have opened an investigation to determine whether houses built near the river complied with safety rules.
The flooded house where nine people died this weekend in Casteldaccia, Sicily. Photo: AFP/Alessandro Fucarini
In a separate incident in Sicily, a 44-year-old man was found dead in his car near Vicari, also in the Palermo region.
He had been trying to reach a service station, where he was the manager, to help a colleague trapped there. A 20-year-old passenger in the car with him is still missing.
Rescue workers are also searching for a doctor, 40, forced by the storms to abandon his car on the road near the town of Corleone after trying to drive to work at the hospital there.
Two other people, a man and a woman, died after their rental car was swept away by a torrent in the region of Agrigente, rescuers said.
Violent winds and strong rain had killed at least 20 other people this week around Italy, especially in the north.
Two were reported killed on Friday, including a 62-year-old German tourist struck by lightning in Sardinia.
Floods in Sicily have closed many roads this week, and mayors ordered schools, public parks and underpasses shut.
On Sunday, military were deployed to check the condition of the main roads on the Mediterranean island.
Six regions remain on high alert for storms.
The severe weather has caused massive damage and disruption across Italy over the past week.
Interior Minister Matteo Salvini posted photos of the devastation in a series of tweets Sunday after also flying over the Alpine town of Belluno.
— Matteo Salvini (@matteosalvinimi) November 4, 2018
“We need 40 billion euros ($45.5 billion) to secure the national territory,” he said.
He pledged to collect and spend that sum but, in a barbed aside to the European Union, said he hoped his plans would not provoke overspending complaints from Brussels.
Italian Prime Minister Giuseppe Conte spoke of “an immense tragedy” during a visit on Sunday to affected areas in Sicily.
Italy's civil protection agency has described the weather lashing the country this week as “one of the most complex meteorological situations of the past 50 to 60 years”.