The family members were all traveling in the same small Lancia hatchback before dawn when it was grabbed by the rushing waters in eastern Sicily.
The woman and three other occupants made it out and to the safety of the riverbank, but her daughter and two other women remained trapped inside and drowned.
Elsewhere on the Italian island, a four-wheel-drive vehicle was also picked up by a raging river, but both occupants were rescued in an operation involving a helicopter.
The incidents occurred as Italy suffered a bout of foul weather over the weekend that has unfurled rain and windstorms across the country, making rivers surge and causing widespread flooding.
Heavy snowfall in the Italian Alps has disrupted communications and electricity supplies, and resulted in the suspension of some train services with neighbouring Austria.
The meteorological conditions were expected to last into Tuesday.