Seven of the injured had life-threatening injuries, according to a spokesman for the national emergency office ONEMI. They were taken to health centers for treatment.
Initial evidence suggests that the collapse was caused by the building's capacity being exceeded, according to police.
"It is an authorized club," Police Chief Hugo Insulza told reporters.
"What happened was that more people were in the club than should have been present," and part of the building structure collapsed, he added, insisting that no stampede took place.
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"There was a crush of people. Even after the venue reached its full capacity, people kept pushing to get in. That led to the collapse of a containment fence that fell on people inside," an ONEMI official said.
The club's administrator was placed under arrest pending an investigation.
A punk concert was taking place at the venue, and an unspecified British band was participating, local media reported.