Spokeswoman Norah West says the injuries are not life-threatening. The injured inmate, who was not identified, was sent to a hospital for treatment after the attack Friday afternoon.
West says 21-year-old Brian Rivas was taken to a maximum security unit, where he will remain while Monroe police investigate. Rivas is serving a 17-year sentence for first-degree assault with a deadly weapon in Pierce County.
The spokeswoman says staffers quickly separated the two inmates.
Inmate movement has been restricted at the reformatory unit of the Monroe Correctional Complex.
The complex is the state's second-largest prison with more than 2,500 offenders.