The two children were walking with their father in the Maccalube nature reserve north of Agrigento when a geyser spewed mud over them.
The father, a police officer, was uninjured, but the girl's body was found shortly afterward while the boy could not be found, the reports said.
He was celebrating his ninth birthday on Saturday, they said.
The Maccalube reserve offers an unusual landscape of small mud geysers that erupt sporadically.
It was closed for part of August because of intense underground activity, press reports said.