Tamaulipas state authorities said in a statement that three inmates have acknowledged to stabbing the victims to death with makeshift knives.
Officials say the suspects told investigators they attacked the six inmates Sunday night because of old grudges between the two groups.
Authorities didn't say if those involved are connected to drug trafficking or what crimes they were convicted for. Tamaulipas state has become a battleground for the formerly allied Zetas and Gulf drug cartels as they fight over turf.