The clashes took place in a mountainous jungle region of the department of Ayacucho where the valleys of the Apurimac and Ene rivers meet known as the VRAE, the military said. The VRAE is Peru`s top coca leaf producing area.
The victims are army sergeants from the anti-insurgent Union Mantaro base that were leading patrols into the jungle searching for guerrillas, the military said.
The deaths come after five soldiers were killed in an ambush in the region on June 4 in an attack also blamed on the Shining Path.
Soldiers will "intensify the search for the criminal terrorists in the zone," the military statement said, adding no further details.
The Shining Path is a militant Maoist organization that carried out terror attacks across Peru in the 1980s and 1990s, with the goal of replacing what it saw as bourgeois democracy with "new democracy."
The group however has withered since the capture of its leader Abimael Guzman in 1992 and a fierce crackdown by then-president Alberto Fujimori.
The remnants, along with a handful of young recruits, number around 400 and have been active alongside gangs of drug traffickers in remote places like the VRAE region.
The clash comes just days before Ollanta Humala, a leftist former army officer who battled the Shining Path earlier in his career, takes office on July 28.
Some 70,000 people were killed between 1980 and 2000 as the Peruvian government crushed the Shining Path and a rival leftist guerrilla group, the Tupac Amaru movement, according to Peru`s independent Truth and Reconciliation Commission. (*)