Adam Burton, 23, and a French tourist were caught posing naked on Wednesday by surveillance workers and were removed from the Unesco World Heritage site, Cusco police said.
A police spokesman told the Press Association the pair were questioned over minor offences "against morality".
The Foreign Office said it was in contact with the Peruvian authorities.
It is understood the men have not been arrested or charged.
A Foreign Office spokesman said: "We are in contact with local authorities in Peru following an incident involving a British national in Machu Picchu."
Surveillance was increased at Machu Picchu in March 2014 after nude photos and streaking became increasingly common at the site.
The Machu Picchu citadel, built by the Inca Empire in the 15th Century, stands at 2,430m (7,972ft) above sea level.
Hundreds of thousands of tourists visit the site, which is one of Peru's main tourist attractions, each year.
In June, 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.
A British man has been been questioned in Peru after posing naked at the Machu Picchu ruins, local police have said.