It depends. If the child was also an Italian citizen at the time of naturalization, he is naturalized with his parents and loses his Italian citizenship.
If the child was born in the jus soli country, he does not lose his Italian citizenship. The exception to this is a naturalization that took place before the 1912 citizenship law went into effect. Most consulates (with the possible exception of Philadelphia) have interpreted the law to mean that all children (even those born in a jus soli country) lost Italian citizenship with their parents before that date.
Where was the minor child born? If in Italy, yes, the minor child loses his Italian citizenship because he is automatically naturalized along with the parents. And this happens even if the parents are in America but the child is still in Italy.
If minor child was born in USA, he loses Italian citizenship if he was born after the parents naturalized. In other words, born to parents who were no longer Italian.