Thousands had gathered at a stadium in Algiers to see rapper Abderraouf Derradji, better known as Soolking, perform when a stampede is said to have broken out at one of the entrances.
Twenty-one people were injured in the stampede and taken to hospital, medical sources told local media outlets.
The concert then went ahead and was carried live on Algerian TV.
Local news site TSA reported that of the five young people killed, three were male and two female.
Video footage posted on social media showed medics carrying a person believed to be a victim of the stampede on a stretcher outside the stadium.
A journalist who was at the concert, Linda Chebbah, told BBC Newsday that from the beginning it looked like something was wrong.
“There were way too many people for this stadium. On the pitch, people were jostling for space. There were so many people at the concert, that I’m not surprised an accident happened.”
Algerian musician Soolking has not yet commented on the incident on social media.