About 20 people packed the first-floor balcony three-deep before it collapsed, concertgoers say.
The incident occurred on Castle Street about 7.45pm last night, where about 1500 people had gathered to watch New Zealand band Six60.
Concertgoers RNZ News spoke to said there were 20 people on the balcony, but they believed it could only hold up to six.
They said people were jumping up and down with excitement as the band began when the deck suddenly gave way, plunging three metres onto the crowd below.
Eighteen people were taken to Dunedin Hospital, two in a serious but stable condition. One has since been transferred to Christchurch Hospital.
The remaining 16 people have been discharged.
Many students at the front of concert said they did not know what had happened until they heard the news this morning.
Some are shocked, but others said no balcony could hold that many people.
A student who lives in the complex where a balcony collapsed said it was a huge wake-up call.
She said her friend was receiving surgery after being injured by the falling balcony.
"It is not nice to see your friends in situations like that at all, and it's definitely a big wake up call, but that it is not what we intended at all. We never thought that that would happen, ever."
She said in retrospect, more security was needed to handle the massive crowd.
Two students who live in the complex said they have friends in hospital who were both on the balcony and below it, and the worst injured were those beneath the balcony.
Otago University Students' Association president Laura Harris said the collapse was deeply distressing, and that people should visit or call the association's support centre, or email firstname.lastname@example.org if they want to talk about what happened.
She said she went to the emergency department last night to support the injured students and their friends, and the mood was sombre.
However, the association could not have done much to prevent what happened, as it did not even know the gig was on, she said
Police said they had been warning people to stop jumping before the balcony collapsed.
Very upset that people were hurt tonight. Massive thanks to the local police and security who were working with us to help keep people safe.— SIX60 (@SIX60) March 4, 2016
Inspector Doherty said there had been some difficulty getting people out initially because the area was congested due to the concert going on and the number of people in attendance.
Worksafe New Zealand will investigate what happened over the next couple of days.
Jennifer Bell was close to where the first-floor balcony collapsed and said people could not move, even if they had wanted to.
"So that's what would have been scary is that even when people knew the balcony was coming down they couldn't have got out the way in time because it was packed. Even if they tried they would have been stuck under there."