Fans were waiting for a performance by the country group Sugarland when the accident happened Saturday night.
Witnesses say Indiana state police took to the stage to issue a weather warning about 10 minutes before the collapse, and some fans had already walked off to seek shelter.
Moments later, the of the stage rigging toppled over, falling onto a VIP section where hundreds of people were sitting in the audience.
Amateur video showed the stage as it collapsed just before 8:45 p.m. The National Weather Service said Sunday that winds were gusting between 60 and 70 miles per hour at the time. In additional to the four people that were killed, police say 40 others injured.
"The degree of injuries for those people ranges from cuts and scrapes to very serious injuries. I want to be very frank, there could be a possibility that we could have other deaths," said David Bursten of the Indiana state police.
One Indiana newspaper was, in fact, reporting a fifth death Sunday, but that report has not been confirmed.
Witnesses says the scene was like a horror movie. Metal crashed down, trapping and injuring concertgoers.
"It's one of those things you see it, and it happens, and you just ask, 'Did it really happen?'" one witness said.
"We looked to the left, and you could see the dust rolling in. And about that time, I turned my head back to the stage. The cover on top the stage started falling, and it took about five seconds and it was down," said another witness.
Indiana state police say people were trapped underneath the stage. Witnesses say many of the concertgoers rushed to those trapped, trying to get them out and using parts of their seats to assemble makeshift stretchers. Emergency responders were on the scene almost immediately, and volunteers helped them lift the framework so people could get out.
"There was a lot of cooperation. You look at the people that put themselves in jeopardy. It's gratifying to know that people at a moment's notice will jump in to help others," Bursten said.
Meanwhile on Twitter, Sugarland put out the following message to followers:
"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."
Fair officials have cancelled all of Sunday's events. Operations are expected to resume Monday with a service for the victims and their families.
Indiana state police warn that the number of injured may rise because some people may have taken themselves to hospitals.