A second bust was also damaged during the tantrum, said the director of the Press Office for Vatican Museums, Matteo Alessandrini.
The damage was minimal.
"The two busts have been damaged but not particularly badly. One lost part of a nose and an ear, the head of the other came off the pedestal," he told CNN.
Repairs for the busts will cost approximately €15,000 ($26,000) and take 300 hours according to Roman news company, Adnkronos.
After the outburst, the man was quickly caught by Vatican police and handed over to the Italian authorities.
He is expected to be charged with aggravated damage.
This is not the first time an unruly tourist has caused trouble in Rome, and unlikely the last. Especially as Covid lockdown measures ease and tourists flood back in pre-pandemic numbers.
For this reason, Vatican authorities are meeting next week to discuss increased security measures for 2023, reported Il Messaggero.
The Chiaramonti Museum is part of the Vatican Museums and is named after Pope Pius VII (Barnaba Chiaramonti), who founded it during the early nineteenth century. It joins the Vatican Palaces to the small Palace of the Belvedere and is lined with hundreds of sculptures.