The tragedy occurred when a wind gust brought down the stage rigging prepared for a country music concert shortly before 9:00 pm (0100 GMT Sunday), police said.
Police officials put the death toll at three, but fair organizers said it could be higher.
"There have been four confirmed deaths. Our prayers are with the families of all affected," The Indianapolis Star newspaper quoted a Twitter message from the state fair as saying.
Emergency crews and fans quickly converged on the collapsed stage and worked to free those who were trapped, the Star reported. The wounded were being treated at Indianapolis area hospitals.
Copyright AFP (Agence France-Presse), 2011