Inmates used sharpened objects, sticks and pipes in the hours-long melee at the prison in northern Mexico Wednesday until guards regained control, El Universal reported Thursday.
The Public Security Ministry said nine of the dead were federal inmates and the remaining 22 had been sentenced in local courts.
Officials were questioning 13 inmates in the incident.
The inmate population of the prison, in Altamira about 20 miles from Tampico, includes members of several drug cartels and allied gangs, El Universal said.
The Tamaulipas attorney general's office was investigating.