Corrections Director Scott Frakes declined to release details of their deaths, which are under investigation.
Peacock and Collins were serving lengthy sentences for child-sex crimes. Peacock had been incarcerated since March 2014 and was serving a sentence of 40 to 50 years. Collins had been in prison since May, 2010 and was serving 66 to 80 years.
Speaking at a news conference, Frakes said 100 to 200 of the roughly 1,000 inmates at the prison were involved in the disturbance that began Sunday afternoon in front of a housing unit at the prison. Two prison staffers were assaulted in the initial disturbance. Frakes says one inmate was shot in the leg by a tower guard, and another inmate was injured by a rubber projectile.
The facility is located about 40 miles west of Rock Port, Mo. The prison is expected to remain on lockdown status until further notice.