Security officials said members of rival drug cartels confronted each other with stones and home-made weapons in the jail north of the city of Monterrey.
Some victims were strangled.
Investigations are under way to establish if some of the prison guards colluded in the fight by unlocking the doors separating two wings of the prison.
Nuevo Leon State Security Spokesman, Jorge Domene said the fight was sparked by the bitter rivalry between the Gulf cartel and the Zetas drug gang.
The two groups are fighting a brutal war for control of the drug smuggling routes to the United States.