A rare and powerful 8.4-magnitude earthquake struck southern Mexico late Thursday, killing at least 15 people as seismologists warned of a tsunami of more than three metres.

The quake hit offshore in the Pacific about 120 kilometres southwest of the town of Tres Picos in far southern Chiapas state, the US Geological Survey said, putting the magnitude at 8.1.

Mexico's seismologic service however gave a magnitude of 8.4, which if confirmed would be the most powerful ever recorded in this quake-prone country.

Chiapas Governor Manuel Velasco said three people were killed in San Cristobal, including two women who died when a house and a wall collapsed. He called on people living near the coast to leave their houses as a protective measure.

“There is damage to hospitals that have lost energy,” he said. “Homes, schools and hospitals have been damaged.”

Tabasco Governor Arturo Nunez said two children had died in his state. One of them was killed when a wall collapsed, and the other was a baby who died in a children's hospital that lost electricity, cutting off the infant's ventilator.

The quake shook a large swath of the country and was felt as far north as Mexico City — 1,000 km from the quake epicenter — where people ran out of their homes in their pajamas as buildings trembled and swayed.

A tsunami warning and the prospect of aftershocks kept the nation on alert.

“Based on all available data ... widespread hazardous tsunami waves are forecast for some coasts,” the Pacific Tsunami Warning Center said.

“Tsunami waves reaching more than three metres above the tide level are possible along the coasts of Mexico,” it said, with lower waves in other countries.

The tsunami warning was for the coasts of Mexico, down through Central America into Guatemala, El Salvador, Costa Rica, Nicaragua, Panama and Honduras, and as far south as Ecuador.

The quake was felt in much of Guatemala, which borders Chiapas.

President Enrique Pena Nieto ordered schools to remain closed Friday in Chiapas and Mexico City so officials could inspect for structural damage.

He said on Twitter he was overseeing the emergency response from the National Disaster Prevention Center's headquarters.

In Mexico City, people ran out of buildings after hearing earthquake warning sirens go off just before midnight (0500 GMT Friday).

“I was driving when the ground started to shake. The car was wobbling!” said Cristian Rodriguez, a 28-year-old driver for ride-hailing service Uber in Mexico City.

“We heard an explosion. Apparently it was a transformer. The streetlights started swinging back and forth,” said Mayaro Ortega, 31, a resident of the capital's north side who went running from her building.

The quake struck at a depth of 33 kilometres, the USGS said.

It is the strongest to hit quake-prone Mexico at least since 1985, when an 8.1-magnitude earthquake in Mexico City killed more than 10,000 people.

The authorities have since instituted a stricter building code and developed an earthquake alert system using sensors placed on the coasts.

Mexico sits atop five tectonic plates, whose movement makes it one of the most earthquake-prone countries in the world.