Strong winds took the stage down Saturday night while fans were waiting for the country band to perform.
Thousands were evacuated from the fairground grandstand to a nearby coliseum.
Authorities said that four people died when the stage crashed down, and the fifth person died overnight at a hospital.
The Marion County Coroner's office identified the victims as Alina Bigjohny, 23, of Fort Wayne; Christina Santiago, 29, of Chicago; Tammy Vandam, 42, of Wanatah; and two Indianapolis residents: 49-year-old Glenn Goodrich and 51-year-old Nathan Byrd. Byrd died overnight.
Officials said 45 people were taken to hospitals after the incident.
After the accident, Sugarland tweeted, "We are all right. We are praying for our fans and the people of Indianapolis. We hope you'll join us. They need your strength."
Concert-goers said opening act Sara Bareilles had finished performing and the crowd was waiting for Sugarland to take the stage when the storm hit just before 9 p.m. They said an announcer alerted them that severe weather was possible and gave instructions on what to do if an evacuation was necessary. But the announcer also said concert organizers hoped the show would go on, and many fans stayed put.
Witnesses said dirt, dust, rain and wind came barreling up the fairground's main thoroughfare minutes later and the stage collapsed.
The fair was closed Sunday. When the Indiana State Fair reopens Monday, there will be a public memorial to honor the victims.
Sugarland canceled their show Sunday at the Iowa State Fair.
The Associated Press contributed to this report.