"Right now, we know we have five people dead -- five minors who have died. We are still at the site," police official Helber Ordonez told AFP.
"There was a rebellion," he said.
Some detainees had set fire to mattresses in one part of the centre "and as a result the blaze started," he said.
Thirty other detainees were hurt and were taken to hospital, emergency officials and local media said. Some were seen being carried to ambulances and municipal vans.
It was not immediately known how many young offenders were in the Juvenile Diagnosis and Rehabilitation Centre in Trujillo, located 500 kilometres north of the capital Lima.
A couple of years ago, the establishment's director complained that although the facility was built to hold 80 minors it had more than twice that crowded inside.
Peruvian television showed images of relatives gathered outside the centre, anxious for news of what was happening inside.
"Please, we want to know the truth. There are people dead, they aren't at the hospital. My son is inside," the mother of one detainee sobbed in a video posted by the newspaper Correo.
Trujillo, Peru's main northern city, has high a high crime rate, much of it linked to gangs and drug traffickers. Pope Francis visited the city in January during a South America tour.
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