The incident happened in the back of a vehicle at the conclusion of a training exercise near Golden State Highway and Templin Highway at around 11:12 a.m.
Five of the inmates working with the California Department of Corrections suffered mild to moderate burn injuries, while the sixth was described as being in critical condition.
All six victims were taken to hospitals in the area for treatment of their injuries. They are all expected to recover.
The crews were working with L.A. County Fire.