"One person passed away last night as a result of injuries," said city spokeswoman Kylie Hatton. "It was a female individual. She passed away after she was taken to hospital."
The temporary scaffolding outside Cape Town's Green Point stadium collapsed shortly before the show, injuring 19 others, 12 of whom needed medical treatment.
"We wish to express our deep sadness and concern for those injured and our heartfelt condolences to the family of the fan who died as a result of her injuries," Linkin Park wrote in a statement on its website.
The band said that they learned about the death following the concert, which went ahead as planned despite the weather.