The Foreign Office said it was looking into the reports, which said a Briton and a French man had been detained after removing their clothes and taking photographs with a mobile phone.
They were taken to a police station and then court, charged with moral misconduct, Peru's news agency said.
The Foreign Office said it was making contact with the Peruvian authorities.
Surveillance was increased at Machu Picchu in March 2014 after nude photos and streaking became increasingly common at the Unesco World Heritage site.
The Machu Picchu citadel stands 2,430 metres (7,972ft) above sea level and was built at the height of the Inca Empire in the 15th century.
Hundreds of thousands of tourists visit the site each year.
In June in a separate incident, four tourists who posed naked on a mountain in Malaysia, including one Briton, were given jail sentences of three days for causing a public nuisance.
