Emergency crews and tourists rushed to the scene to try to help the family. But when his parents tried to rush to his rescue, they too were were sucked in, police said.
His father, then his mother, both fell in as they tried to rescue him. They are understood to have fallen 5ft but it is not yet known whether they were killed by the fall or by toxic gas fumes.
The bodies were retrieved a short while later and placed in body bags before being taken away by ambulance. They've determined the fields had risen by about 12 inches over a decade.
Three members of an Italian family died visiting a volcanic field Tuesday after an 11-year-old boy entered an off-limits area.More news: Thousands without power in coastal Georgia from severe storm
Pozzuoli's mayor, Vincenzo Figliolia, said he was in "deep pain" over the tragedy, according to La Repubblica.
The father ran to his aid when the ground gave way beneath him. "I was at the Solfatara for work, along with other visitors". I continue to think about that family and that poor boy crying and asking for help'.
"I'm upset about what happened inside the Solfatara volcano", said local mayor Vincenzo Figliolia. "I express my closeness from the community of Pozzuoli to the victims' family", he said.
Solfatara is a dormant volcano which still emits jets of steam and sulfurous fumes.