Fourteen were hospitalized, the Belfast Telegraph reported. As many as 50 or 60 were treated by paramedics who responded to the scene Thursday night.
Whether any of the young people were suffering from the ill effects of drugs was not known.
The event at the arena was a concert by Hardwell, or Robbert van de Corput, a young Dutchman ranked the world's top disc jockey in a magazine poll last year. When tickets went on sale in mid-January, some young fans camped out overnight at the arena.
Adrian Doyle, the Odyssey's manager, said ticket-holders who were visibly drunk were not admitted.
The Ambulance Service declared a major incident.
"We believe the majority arrived suffering from too much alcohol," a spokesman said.