The boy's 45-year-old father attempted to pull him up and was sucked into hot mud, ANSA reported. When the boy's 42-year-old mother tried to save her husband, she was also sucked in.
The couple's other son, a 7-year-old boy, managed to get to safety.
A witness to the incident told la Repubblica newspaper he saw the 7 year old crying and asking for help.
"I saw a child run crying, I did not think I was facing the worst tragedy of my life, I'm a father, too," Diego Vitagliano said.
Authorities said it wasn't immediately clear if the family was overcome by gases or molten lava in the area, The Associated Press reported.
The crater is located in the Phlegraen Fields, a sprawling constellation of ancient volcanic craters frequented by Italian school children and tourists from around the world. The fields are scorching hot only a few inches below the surface.
"I've been here for forty years and such an accident has never happened," Armando Guerriero, owner of a nearby bar located near the entrance to the volcano, told ANSA.
Geologists monitor the area by checking temperatures and chemically analyzing gases. They've determined the fields had risen by about 12 inches over a decade.
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