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.

It clears the way for the team to make their debut appearance the tournament, which will be held in Gabon from 14 January to 5 February.
After the news emerged, thousands lined the streets of the capital, Bissau, to watch the squad parade by on Tuesday.
Guinea-Bissau play Group A rivals and hosts Gabon in Saturday's opener.
They will also face Burkina Faso and Cameroon in the group stage having achieved a fairytale qualification - one of the biggest shocks in Nations Cup history.
Yet the bonuses that had been promised them for qualifying remained unpaid, leading to the players going on strike at the weekend.
It was only settled after a delegation of three players went to see the country's president, Jose Mario Vaz, Portuguese news agency Lusa reported.
They have since all received between 10,000 and 23,000 euros in outstanding fees, Lusa added.
"In the early hours of Sunday, the players received everything they had to receive," a government spokesman told the agency.
A charter plane, borrowed from Congo-Brazzaville, was due to fly the team to Libreville on Wednesday.
The former Portuguese colony frequently beset by coups, eliminated former champions Congo and Zambia in qualifying last year.
They were a Leicester-like long shot when the qualifiers began, having previously won only four matches in Nations Cup and World Cup qualification combined since first entering international competition just 22 years ago.
A British man has been been questioned in Peru after posing naked at the Machu Picchu ruins, local police have said.
[NEXT_CONCEPT]
Guinea-Bissau's players have ended their strike after being paid outstanding wages, four days before the start of the Africa Cup of Nations.