The woman, who has not yet been identified, was killed under a banner advert for Lucozade when gale force winds caused a structure to collapse.
"Following our performance tonight at Cape Town Stadium, we were advised that several people were injured as a result of the collapse of an advertising tower erected by Lucozade in the parking area outside the venue," read a statement on the band's website.
"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.
"Though we have had no relationship with the sponsor or the entity responsible for erecting the structure, we take the safety of our fans very seriously and our thoughts are with all of those who were affected by this tragedy."
Dionne Domyan, spokeswoman for promoter Big Concerts, added: "We would like to thank the City of Cape Town, the South African Police Services, and all the medics, doctors, and disaster risk personnel for their swift and professional response to this accident."
She later confirmed that structural engineers had "pre-approved and certified safe" the advertising tower
The band have confirmed that their tour will continue with the next show at Johannesburg this Saturday.
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