Ana Clara Benevides, 23, became unwell at the Nilton Santos stadium, event organizer T4F SHOW3.SA wrote on Instagram. It said she was promptly attended by medical staff, and then taken to an on-site medical station, before being transferred to the Salgado Filho Hospital, where she died.
Rio state health service said she arrived at hospital with her heart stopped. Her cause of death is unknown, and will be investigated.
Swift - who is scheduled to perform in Rio on Saturday and Sunday, followed by three shows in São Paulo between November 24 and 26 - offered condolences to Benevides' family and friends.
Some 60,000 fans had gathered for Swift's sell-out concert at the stadium, which is located far from Rio's breezy picture-postcard beaches in a hotter northern neighbourhood.
The show took place on the same day that Rio recorded its highest-ever reading of the so-called heat index, which combines temperature and humidity, at 59.3 degrees Celsius (138.74 degrees Fahrenheit).
Reuters video showed fans suffering in the heat on Saturday (November 18) as they waited to get in the show later.
Reuters