Irish foreign minister Charlie Flanagan told reporters in Dublin that all five of the dead were in the US on temporary visas.
A 21st birthday party was under way in the building in the university town of Berkeley at the time of the accident, he said.
Many of the wounded have critical, life-threatening injuries, said Officer Jennifer Coats, a Berkeley police spokeswoman.
Police received a call about the incident shortly before 1am local time (9am BST). Officers arrived to find that the balcony on the fourth floor of the building had disintegrated.
Television footage showed that the balcony fell onto the one below it, on the third floor.
The building in the heart of Berkeley has apartments in the upper floors and shops at ground level. The area, just blocks from the University of California, Berkeley, is dotted with museums, restaurants, coffee shops and chain stores.
The Library Gardens apartments were built in 2006 and are a block from campus, the Los Angeles Times reported.
Ireland's department of foreign affairs said it was trying to contact families of the victims and could not give details of their identities. Four died at the scene and one in a hospital, Mr Flanagan said.
Irish president Michael D Higgins said in a statement that he had "heard with the greatest sadness of the terrible loss of life of young Irish people and the critical injury of others in Berkeley, California today.
"My heart goes out to the families and loved ones of all those involved."
Ms Coats said officers are still investigating and she does not have information on how the collapse occurred or what the people were doing on the structure at the time.
Jerry Robinson, who lives nearby, told San Francisco news station KGO-TV that he had just left a movie theatre when two hysterical people flagged down his car asking for a ride to hospital to check on injured friends.
"They were all trying to notify parents, and things like that," he said.
"They were trying to figure out from each other who was on the balcony and what their condition was."
Police are working with fire officials and building inspectors to try to determine what caused the accident, Ms Coats said.
"We don't have a lot of specific detail at this point because they (investigators) are still trying to work through it all," she said in a telephone interview.
Mr Flanagan said the Irish consul general in San Francisco would be providing assistance to those affected.