Officials said they were able to identify him and the woman he was with from photos and footage published online.
The BBC reported the individual faces a large penalty fine or a jail term of up to five years if he is charged and convicted.
In the video, he is seen carving "Ivan + Hayley 23" – believed to be the pair’s names, but not confirmed by officials – into the wall of the ancient monument.
The incident sparked widespread condemnation in Italy and across the globe, as well as prompting G Adventures founder Bruce Poon Tip to launch an appeal to locate the couple to offer them a trip to the operator’s inaugural GX Summit in Peru later this year in a bid to educate them to become more conscious travellers.