Pinal County authorities say the source is believed to be contraband prisoner-made alcohol.
They say the process to confirm botulism takes time, but proactive treatment can begin after consultation with the Centers for Disease Control and Prevention.
Once the CDC receives preliminary confirmation that botulism poisoning may have sickened individuals, the CDC authorizes the release of anti-toxin to the state.
The CDC has released the anti-toxin to the Arizona Department of Health Services, which is delivering it to the medical providers who are treating the affected inmates whose names haven't been released.
Authorities say three of the four inmates are reported to be in stable condition with the condition of the fourth undisclosed.