The three were making their way home from a family meal, along with four other relatives, when the tragedy happened as they crossed a bridge over the swollen Asinaro river in the early hours of Sunday morning, Live Sicilia reported.
The other four passengers in the Ypsilon 4X4 survived while Antonino Restuccia, the 32-year-old driver and cousin of the child who died, was arrested for manslaughter.
The victims were named as Alessandra Tumminieri, 33, Maria Gioelli, 67, and seven-year-old Marisol Latino.
Heavy rains battered much of Italy, swelling rivers and flooding fields and roads, while alpine areas saw abundant snow, over the weekend.
The level of the river Tiber in Rome neared the top of its arches by Ponte Milvio bridge, while the river Arno in Pisa was also swollen
Rain is expected to continue until Tuesday, with the north-east regions being the worst affected, while more snow is forecast in the Alps.