The tourists had been climbing the 'Statue of the two Hercules' on Friday night when they involuntarily broke off a piece of the marble crown that sits on top of the monument, the Milan edition of Corriere della Sera reported.
By Sunday police had identified the two perpetrators. On Monday, technicians will assess the damages to the statue.
Situated under the portico of the 13th century Loggia dei Militi, the monument depicts two statues of Hercules holding a large shield. It is considered to be a symbol of Cremona itself, which is said to be founded by the mythological hero.
Completed in 1700, the statue was originally placed on top of the city gates before being moved to its current location in 1962.
This isn’t the first time Italy’s monuments have fallen victim to careless tourists.
In February Dutch football fans damaged one of Rome’s most treasured fountains, the Fontana della Barcaccia, at the foot of the Spanish steps, during rioting ahead of a Europa League match against AS Roma. The damage was estimated at €5 million.
In 2013, an American tourist accidentally snapped a finger off a 600-year-old statue in Florence’s Galleria dell’Opera di Santa Maria del Fiore.