The 37-year-old inmate was pronounced dead at the scene about 5 p.m. Monday, nearly seven hours after the incident began, the Illinois Department of Corrections said. His name hasn't been released.
The hostage, a 62-year-old female employee, was rescued and was being evaluated by medical personnel.
The agency says around 2,200 male inmates in the prison remain on lockdown and the facility is secure.
Corrections officials say the offender was serving a sentence for aggravated criminal sexual assault and aggravated kidnapping. The crimes took place in Cook County.