|At least 35 people died in the quake|
Tsunami waves hit the southern coast of Mexico after a 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 ranged between 4.5 and 5.7 in magnitude, the US Geological Survey said.
At least 35 people died in the quake
Mexican President Enrique Pena Nieto said the quake was the biggest his country had seen in a century.
The governor of the southern Oaxaca state said at least 23 people died there.
Two children were killed 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.
Seven people were killed in neighbouring Chiapas state - among them two women who died in San Cristobal when a house and a wall collapsed.
|People gathered in the street in Mexico City in their pyjamas|
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.
Mr Pena Nieto said a million people had initially been left without power, but 800,000 had now had it restored.
The quake struck off Mexico's southern coast
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.
Buildings in Guatemala were shaken by the tremor.
Firefighters in the street of Mexico city after earthquake
"I had never been anywhere where the earth moved so much," said 31-year-old architect Luis Carlos Briceno, who is visiting Mexico City.
"At first I laughed, but when the lights went out I didn't know what to do. I nearly fell over."