This was reported by the publication Milenio with reference to the head of the State Coordination Center for Civil Protection Antonio Amaro Kansino.
According to authorities, more than 2,000 homes in 85 municipalities were damaged.
Six dead were previously reported.
Oaxaca Governor Alejandro Murat called on federal authorities to declare a state of emergency in the region.
An earthquake of magnitude 7.3 occurred in Mexico on June 23.