The quake, which was felt as far Guatemala City, had a preliminary magnitude of 8.0 and depth of 33 km, according to the Pacific Tsunami Warning Centre.
It struck off the Pacific Coast 120 km southwest of Tres Picos, Mexico, which is 1,000 km southeast of Mexico City, reports CNN.
The Tsunami Warning Centre advised the public that tsunami waves could hit within three hours off the coasts of Mexico, Guatemala, Panama, El Salvador, Costa Rica, Nicaragua, Honduras and even Ecuador.
The tremor led to power cuts in the Mexican capital which was put on seismic alert.
CNN attempted to contact two seaside hotels in the Mexican state of Chiapas, next to the border with Guatemala, but the lines appeared to be down.