The victims, all 18 to 25 years old, were knocked down and trampled by a crowd at a large hall, Cadena Ser radio network/Agenzia Giornalistica Italia reported Thursday.
Three women suffered cardiac arrest and died, officials said.
Police said the crowd of about 10,000 people rushed to leave the building after a flare was reportedly fired about 4 a.m. All but one of the doors in the building had been locked.
An investigation was under way.
Celebrity Families of 2014 [PHOTOS]