"The protesters surrounded a group of nine police that were lifting a road blockage on the Arequipa-Puno road, and took them hostage," a police officer said.
Local media reported that protest leaders wanted to swap the hostages for 14 demonstrators detained earlier.
Meanwhile, hundreds of public teachers took to the streets of Lima on Friday to demand the government withdraw an education reform plan, which they say will leave hundreds of teachers unemployed.
Farmers, builders and people from impoverished regions have staged sometimes violent protests this week to demand that the centre-left Garcia government invest more in social projects and improve working conditions.
Garcia took office for a second time a year ago, pledging to claw Peru away from a "social catastrophe" by creating jobs and ending growing inequality.
His first term in power ended in 1990 amid economic turmoil and widespread protests.