The Arizona Department of Corrections says 53-year-old Lino Flores was not breathing and suffered traumatic injuries when he was discovered around 2 p.m. Saturday at the Eyman prison complex.
Despite efforts by staff to administer aid, Flores was pronounced dead at the scene.
Investigators are questioning fellow inmate Julio Salazar.
DOC officials say Flores and the 32-year-old Salazar were both in the recreation area of their housing unit at the time of the incident.
Flores was serving a life sentence for first-degree murder, second-degree murder, sexual assault, possession of a deadly weapon and assault with a dangerous weapon.
Salazar is serving sentences for murder and manslaughter.