Several other substantial tremors followed in the same region
Authorities in Mexico say at least 58 people are now known to have died after an earthquake hit the country.
A baby whose ventilator stopped working when a hospital suffered a power cut was among the victims.
The magnitude 8.1 earthquake struck shortly before midnight local time.
The Pacific Tsunami Warning Centre said waves of 3.3ft (1m) had been measured off the port of Salina Cruz.
Multiple aftershocks ranging between 4.5 and 5.7 in magnitude were recorded, the US Geological Survey (USGS) said.
Mexican President Enrique Pena Nieto said the quake was the biggest his country had seen in a century.
The death toll includes two children in the state of Tabasco.
Its governor, Arturo Nunez, said one was a baby who died at a children's hospital which lost power, causing the infant's ventilator to stop working.
In neighbouring Chiapas state, two women died in San Cristobal when a house and a wall collapsed.
"Homes, schools and hospitals have been damaged," state governor Manuel Velasco said.
In Juchitan in Oaxaca state, parts of the town hall, plus other buildings including a hotel and a bar were reduced to rubble.
People in the capital, Mexico City, ran out into the street in their pyjamas after the tremor shook buildings.
Enrique Pena Nieto said a million people had initially been left without power, but 800,000 now had it back.
The quake struck at a depth of 43 miles (69 km), 76 miles (123 km) southwest of the town of Pijijiapan.
It posed a potential tsunami threat to the Pacific coastlines of countries including Guatemala, El Salvador, Costa Rica, Nicaragua, Panama and Honduras, the US Tsunami Warning System said.
The Irish embassy in Mexico says Irish citizens should follow the advice of local authorities:
Additional reporting: IRN