Officers detained Angel Villaverde, 52, at Lima airport on December 26, a police source told the news agency AFP.
Villaverde was born in Peru but has lived in Sweden for 20 years, according to Swedish media.
He was arrested, the source said, “because he is wanted by a Lima criminal court for a crime of terrorism.”
Police would give no details of exactly what Villaverde is accused nor whether he is suspected of links to armed rebel groups in the country.
His arrest came to light after his family talked about it to Swedish media. They said he was returning to Peru to visit his ill mother.
It was his first visit to his native country since he left as a refugee in 1995, according to a newspaper in the Swedish town of Sundsvall where he is a municipal leader.
— Sundsvalls Tidning (@STnu) December 29, 2015
A tweet showing the politician by the town's local newspaper, which broke the story
That was during a period of attacks in Peru by the Maoist group Shining Path and another leftist revolutionary movement, MRTA.
The Swedish foreign ministry said it was seeking information from Peruvian authorities via its embassy in Chile.
“We have confirmation that a 52-year-old Swede has been detained in Lima,” ministry spokesman Anna Ekberg told AFP.
The Peruvian police source said Villaverde was being held in cells at the Palace of Justice in Lima and would go before a judge in the coming days.