"If (the crime) has been proven, the alleged Peruvian could go to prison for seven to 10 years," national prosecutor Jose Pelaez told the TV Peru Noticias television channel late on Monday as he confirmed Barrios was under investigation.
Pelaez added that the defender's alleged father, Peruvian former footballer Angel "Maradona" Barrios, is also being investigated as an accomplice.
The possible scandal came to light when Peru met Ecuador earlier this month during the Under-20 championship in the Argentine Andean region of Cuyo.
Media reported that members of the Ecuador side said they had seen the defender playing in their country and that his name was not Barrios.
They said he was identified by a member of their country's congress as Juan Carlos Espinoza Mercado, a 25-year-old Ecuadorean.
Barrios, whose now annulled identity document said he was born in Sullana in northern Peru, joined Peruvian first division side Juan Aurich a year ago as a junior.
As a 17-year-old allegedly born in 1995, he was picked for the Peruvian Under-20 team for the South American championship, from which the top four countries qualify for the Under-20 World Cup in Turkey later this year.
Barrios senior - who bears a resemblance to Argentine great Diego Maradona - has said his alleged son has dual nationality, was born in Ecuador and played there when he coached Ecuador's Liga de Loja in 2010.
"My son cries and wants to quit football," he was quoted as saying by Peru's RPP Noticias about the defender's reaction to the scandal.
Juan Aurich have rescinded Max Barrios's contract, while Peruvian authorities have annulled his birth certificate and identity document.
South America's football governing body CONMEBOL and the Peruvian and Ecuadorean federations, the FPF and FEF, are investigating the case.
Peru lost 2-1 to Ecuador and Barrios was sent off for a second booking near the end but they qualified for the six-team final group currently being played.