The band were due to play a set at the Indianapolis event on Saturday night but strong winds caused the stage to collapse, killing at least four people and injuring 40 more.
Sugarland's singer Jennifer Nettles admitted that the band were "stunned and heartbroken" following the incident, saying: "We hold those injured in our prayers at this very sad time. There are no words. It is tragic."
The band have since said that they will pay tribute to those affected by the accident, but are waiting until the victims' families have had more time to properly mourn their loved ones.
"We are in the process of planning a private memorial in Indiana, to honour those fans who died," the band said in a statement on Tuesday.
"We would first like to hold space so that their families can have time to go through their own services and memorials. Until that time we are holding vigil for them. We join them on their mourning benches."
Sara Bareilles, who finished a performance at the Indiana State Fair just moments before the collapse, described the incident as a "bad dream".
Lady Antebellum and Janet Jackson cancelled their respective sets following the tragedy.
Watch footage of the stage collapse at the Indiana State Fair below:
Warning: contains upsetting scenes