Spanish officials say that two more people were seriously injured at the gathering at the Madrid Arena.
It was not immediately known what caused the crush, but reports suggest the panic began after a flare was thrown in the crowd.
The building, which can house up to 10,000 people, was evacuated after the incident.
Two of the victims were 18 years old, while the third was 25, Spanish police say.
“There was a human crush at the only exit they had because the others were sealed off,” a partygoer – who gave her name as Sandra – told Spain’s Cadena Ser radio station.
The stampede recalled a mass panic at the Love Parade music festival in Germany that killed 21 people in 2010.
Updates will be available each hour on the hour.