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2:07 PM
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The United States Geological Survey (USGS) said the quake had a magnitude of 7.4 and put the epicentre at 15 miles (25km) east of Ometepec, in Guerrero state.
Witnesses in the capital, Mexico City, said the tremor sent office workers rushing out onto the streets.
Some 500 houses were damaged in Guerrero state, according to the state's governor, local TV reported.
Angel Aguirre told Milenio television that so far there were no casualties in Guerrero state or neaby Oaxaca state, adding that authorities were checking schools and public buildings near Ometepec.
The director of the country's seismological service, Carlos Valdes Gonzalez, said that there had already been some six aftershocks and further ones could be expected in the next 24 hours.
He said one of the aftershocks had already registered a magnitude of 5.3.
The BBC's Will Grant, in Mexico City, says buildings swayed for at least a minute in the capital.
A pedestrian bridge reportedly collapsed and crushed a microbus in Mexico City, but there were still no reports of deaths.
Office workers and residents were sent running into the streets in wealthy districts and poor neighbourhoods alike, he reports.
Thundering walls
Samantha Rodriguez, a 37-year old environmental consultant, was evacuated from the 11th floor of an office block.
"I thought it was going to pass rapidly but the walls began to thunder and we decided to get out," she said.
In the capital, Mexico City, some children were evacuated from their schools Sirens could be heard across the city, and police helicopters are crisscrossing the skies.
"I swear I never felt one so strong, I thought the building was going to collapse," said Sebastian Herrera, 42, a businessman from a neighbourhood hit hard in Mexico's devastating 1985 earthquake, which killed thousands.
Mexico City Mayor Marcelo Ebrard's Twitter account said the water system and other "strategic services" were not experiencing problems and no damage was reported in the central or northern areas of the city.
Mobile phone networks have been affected, our correspondent says, and people have had trouble contacting their loved ones.
Gabino Cue, the governor of Oaxaca state, next to Guerrero state, said via Twitter that the quake had caused cracks in school buildings and damaged roofs in one part of the state.
The USGS said the epicentre was 11 miles (18km) underground.
The US president's daughter, 13-year-old Malia Obama, was on a school trip in Oaxaca, south-western Mexico. A White House official said she was safe and had never been in danger.
