More than 40 people were injured in the collapse on Saturday night, just minutes before the country duo Sugarland was set to begin performing, Indiana State Police said.
Some of the injuries were extremely serious, and more people could die, said State Police Sgt. Dave Bursten at a news conference.
"That possibility is there," he said
Concert officials had informed spectators prior to the show that the concert might have to be postponed due to the weather, but a strong gust blew the stage over before any official evacuation order was issued.
Indiana Governor Mitch Daniels called the collapse "freakish," saying at the news conference that a storm was anticipated but the blast of wind that whipped through the grandstand area was unexpected.
One of those killed was stagehand Nate Byrd, 51, who was on the stage rigging to run the show's spotlight. He died on Sunday at Methodist Hospital.
Killed on the scene were Tammy Vandam, 42, of Wanatah, Indiana; Glenn Goodrich, 49, of Indianapolis; Alina BigJohny, 23 of Fort Wayne and Christina Santiago, 29, of Chicago, according to the Marion County Coroner's office.
State fire marshals and the Indiana Occupational Safety and Health Administration are investigating the collapse, authorities said.
An amateur video posted on YouTube showed a heavy gust of wind blowing down the stage rigging. People in the crowd can be heard screaming.
Spectators tried to hold up parts of the collapsed stage that fell into the standing area below to help anyone who might be trapped, eyewitnesses said.
The fair was closed on Sunday but expected to reopen on Monday with a memorial service for the victims.
"It's a very sad day at the State Fair and our hearts are breaking," said the fair's executive director Cynthia Hoye.
Sugarland sent a Twitter message on Saturday night about the incident, saying: "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."
The governor said his wife Cheri Daniels and one of their daughters were at the concert but were not injured.
The Hoosier Lottery Grandstand at the state fairgrounds can seat more than 15,000 people.
No decisions have been made about the rest of the fair's concert schedule that includes performances by Janet Jackson and Maroon Five, authorities said. (S)