About 400 inmates were involved in the fighting.
Bill Lamoreaux with the Arizona Department of Corrections said officers inside the prison broke up the brawl and were working to determine what caused it, KGUN-TV, Tucson, reported.
Seventeen of the injured, including two staff members, were transported to area hospitals for treatment of what were described as non-life-threatening injuries.
Lamoreaux said some inmates were treated at the prison but provided no other details.
"We had every available staff member on the unit, and we have other staff from other units that responded -- good response from all staff," said Daniella Stemple, deputy warden of the Whetstone Unit.