The inmates escaped through a tunnel dug out from the prison’s carpentry workshop to a perimeter fence.
The prison director and two other employees are being held over the incident at the facility in Coahuila, the state’s attorney general said.
A massive manhunt is under way, and the US authorities are on alert in case any escapees attempt to cross the border.
Some 132 men managed to escape from the prison in the city of Piedras Negras, which borders Eagle Pass in Texas to the north.
One by one, the inmates fled through a tunnel measuring 2.9 m (9.5 ft) deep and 7 m long, attorney general Homero Ramos said in a statement broadcast on local TV.
The state government has offered rewards of 200,000 pesos ($15,600) for information leading to the arrest of each prisoner.
This is not the first time such a mass breakout has taken place in Coahuila, but it is by far one of the biggest in recent years.
Such events only go to underline further to the incoming government of President Enrique Pena Nieto the dire state of the prison system in Mexico.
Enrique Pena Nieto is to take office on 1 December. However, prison reform is not expected to be one of the main priorities of his government.
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