The majority of victims suffered stab wounds, said Tracey Martinez, spokeswoman for the San Bernadine County Fire Department.
"The wounds [range] from stab wounds to cuts and bruises to large lacerations to the body area," she told CBS Radio News.
Five were airlifted to hospitals for treatment and the others were taken by ambulance.
There were no immediate reports of injuries to guards or other authorities who responded to the rioting shortly after 8 p.m.
"The California Department of Corrections is currently investigating the incident," Martinez said. "At this time it's unknown the reason or the cause that started the riot."
The prison yard was secured at 10:30 p.m. and prisoners were locked down, Martinez said.
"There was a small content fire inside of a guard shack," said Martinez. "We did douse the fire from outside of the correctional facility with water."
The 262-bed facility is run by the privately held Cornell Companies, of Houston, one of the country's largest private prison operators. The prison handles minimum-security male offenders.
Baker is about 160 miles east-northeast of downtown Los Angeles.