The 54-year-old was attacked after dropping his grandson off at the nursery in Arrone, a town near Terni, Il Messaggero reported.
Forestry workers are now hunting for the boar, which fled the scene. The nursery is close to a green area along the Nera river.
The wild boar population in Italy has grown in recent years alongside a rise in demand for their luxury meat, which can be found in many butcher’s shops.
Hunting for boar is also a popular pastime, and although there have been a number of cases of hunters being attacked, it is rare to hear of random attacks against other members of the public.
There was a spate in 2013 when the animals ransacked gardens and parks in the northern city of Genoa and in one case, ate a pensioner’s dog.
Most deaths associated with boar-hunting, however, are caused by hunters accidentally shooting another person.
In 2010, Giuseppe Orlando della Gherardesca, an heir to one of Italy's oldest aristocratic families, was killed in such an incident.