The museum says the man walked off without telling anyone what happened, but later turned himself in.
CCTV footage has captured the moment a tourist attempted to snap a photo with an artwork – but instead managed to break off part of the 19th century statue.
The man is seen posing for a photograph beside the sculpture of Paolina Borghese Bonaparte as Venus Victrix during a visit to the Antonio Canova Museum in Possagno, Italy, on 31 July.
As he gets up, he accidentally manages to snap off part of the artwork.
The man then examines the damage and walks up and down before casually leaving the room.
He did not report what had happened, the museum said in a Facebook post.
It was only when museum staff spotted the damage that the alarm was raised.
The museum said two of the statue’s toes were damaged.
Police said he was an Austrian man who was part of a group of tourists visiting the museum.
He later turned himself in after reading about the incident in Austrian newspapers, and apologised for his “irresponsible behaviour”.
The museum houses the work of Italian Neoclassical sculptor Antonio Canova.
The statue is the original plaster version of the celebrated marble statue which sits in the Galleria Borghese in Rome.
Experts are planning to restore the damaged piece.