The boy was hit by the lightning bolt late on Thursday morning after being unable to hear a warning from tour guides to close his umbrella, Il Messaggero reported.
The boy was visiting the famous volcano, which devastated the city of Pompeii after an eruption in 79 AD, with his mother and sister when the accident happened, the newspaper said.
He is now in intensive care at San Leonardo di Castellammare di Stabia hospital in Naples.
The accident came a day after a man was killed by lightning outside a cemetery in Latina, a town south of Rome.
Italy has been hit by sporadic, but heavy, downpours and thunder and lightning this week, with parts of the country being flooded.
Storms in Italy often prove to be treacherous. In July last year, a 12-year-old boy died after being hit by lightning while playing football on the beach.
Later that summer, 40,000 lightning strikes were recorded during a single day of storms.