The public safety department of Tamaulipas state, where the prison is located near the border with Laredo, Texas, said 141 inmates got out through a service entrance used by vehicles, "presumably with the assistance of the prison staff."
The department said the prison's director could not be located, adding that he and other officials were under investigation.
Eighty-three of the prisoners were being held for trial or had been convicted of crimes like theft, assault and other state offences, while 58 were being held on federal charges, which include weapons possession and drug trafficking.
Tamaulipas has been plagued by a steady wave of violence tied to turf battles between the Gulf and Zetas drug gangs, but it was unclear whether members of those groups were among the escaped inmates.
States like Tamaulipas have said in the past they are not prepared to handle highly dangerous federal prisoners, and again on Friday the state urged the federal government to take charge of such inmates.
"The state does not have the capacity to prevent them escaping," the department said in a statement.
The federal Interior Department blamed the breakout on local authorities, saying they did not properly guard the facility.
"The absence of effective methods of guarding and control by local authorities is deplorable, and it has caused frequent escapes from prisons that put the public at risk," the department said in a statement.
It called on state authorities to clean up their prison and judicial systems by increased screening and vetting of corrections officers. In past cases, prison guards — often underpaid or under threat from gangs — have been implicated in prison escapes.
Federal police and soldiers were dispatched to patrol the area, and a search for escaped prisoners was begun.
The jail break apparently occurred in the pre-dawn hours Friday.
The escape came on the same day that federal Public Safety Secretary Genaro Garcia Luna addressed a graduating class of new prison guards, underlining the urgent need to professionalize correctional forces.
"We are making a historic effort to build a new prisons model, that will treat prison staff as efficient public servants," Garcia Luna said.
The new guard recruitment programs, supported in part by the U.S. government, include increased training, screening and vetting of guards.