The fight broke out at a prison in Reynosa, a city near the US border in the northeastern state of Tamaulipas.
"Two groups of prisoners were involved in a clash, using weapons such as clubs, stones and shanks," the state government said in a statement.
"Nine inmates died and two were wounded."
The riot broke out on visitation day, and guards "focused their efforts on protecting (inmates') families," it said.
State police were sent in to bring the brawl under control, firing shots in the air to break it up.
Mexico's overcrowded prisons are plagued by riots, revenge killings and jailbreaks, and powerful gangs often hold de facto control inside.
Last month, 28 inmates were hacked to death by their rivals at a prison in Acapulco, a resort town on Mexico's Pacific coast.
The prison system in Tamaulipas, a state racked by the deadly violence of Mexico's drug cartel wars, had already made bad headlines twice this year.
In March, 29 inmates escaped through a tunnel from a prison in Ciudad Victoria.
And in June, seven people were killed, including three police, when officers stormed the same prison to regain control from inmates who had been stockpiling guns.