The tourists had been climbing the 'Statue of the two Hercules', in Cremona, on Friday night when they involuntarily broke off a piece of the marble crown on top of the monument.
The two perpetrators have been identified by the police, 'The Local' reported.
Situated under the portico of the 13th century Loggia dei Militi, the monument depicts two statues of Hercules holding a large shield.
Completed in 1700, the statue was originally placed on top of the city gates before being moved to its current location in 1962.
Technicians have since visited the site to assess the damage caused to the statue.