Cheerleading coach Meagan Toothman, 24, from Ohio sustained serious head injuries in the tragedy and will undergo surgery today to harvest her organs before she is allowed to be "at peace".
"Late last night it became apparent that our Meagan was no longer with us," Toothman's family said in a statement.
"The decision was made to allow her to be at peace. This afternoon she is scheduled for a surgery that will provide gifts of sight, health, and life to dozens who are in need."
The statement continued: "The outpouring of love and hope was more than we could possibly have expected and was an inspiration to all of us to keep her fighting. We hope that she will continue to touch more lives in the same way through her passing."
Strong winds caused the stage to collapse at the Fair on August 13 shortly before Sugarland were due to perform. Four people were killed immediately.
The band's singer Jennifer Nettles later said that she was "stunned and heartbroken" by the event.
Sugarland have since announced plans to hold a private memorial concert to honour those killed and injured by the collapse at a later date.
> Sara Bareilles: 'Indiana stage collapse felt like a bad dream'
> Ryan Seacrest, Kelly Clarkson, LeAnn Rimes pay tribute to Indiana victims
Watch a news report on the stage collapse at the Indiana State Fair below (Warning: contains disturbing scenes):