The quake struck south of the Pacific resort of Acapulco, between the states of Guerrero and Oaxaca, and was followed by several aftershocks, the US Geological Survey said. Initially it had estimated the magnitude at 7.9.
Guerrero governor Angel Aguirre told state radio that some 1,600 houses in four municipalities of the coastal region known as the Costa Chica had been damaged.
He said that authorities were checking schools and public buildings around Ometepec, a town of 20,000 nearest the epicenter.
Many houses showed signs of damage in Ometepec while patients of the main hospital were evacuated into a garden, including women in labor.
The White House said President Barack Obama's 13-year-old daughter Malia, who is on vacation in Mexico, was safe.
"In light of today's earthquake, we can confirm that Malia Obama is safe and was never in danger," said Kristina Schake, spokeswoman for First Lady Michelle Obama.
In Mexico City, buildings swayed, telephone and power lines were cut off and traffic lights stopped working as office workers rushed onto the streets.
Local media reported one person was injured when a pedestrian bridge collapsed on an empty bus in the north of the city.
It was one of the strongest quakes to shake the capital since 1985, when an 8.1 earthquake left between 6,000 and 30,000 dead, according to officials and rescue organizations respectively.
"We were told to evacuate," said office worker Francisco Bernal, standing in the street. "The earthquake was strong but now we're prepared, unlike in 1985."
"I stood up when I saw the lights moving," said Ana Fernandez, another office worker in the central Roma district. "Our boss told us to get out and we followed instructions not to shout, run or push. I was really scared but I made myself stay calm."
German tourist Gernot Nahrung said he was in the city's Chapultepec park and did not feel the long swaying movement of the quake, which lasted several minutes. "My mum told me: 'It's shaking, it's shaking,'" he said.
Mexico City Mayor Marcelo Ebrand said no serious damage was visible during a helicopter survey.
The mayor's Twitter account said the water system and other "strategic services" experienced no problems.
Some windows broke at the city's international airport, and the monorail between the two terminals was stopped temporarily.
The quake's epicenter was 12.4 miles (20 kilometers) deep, 100 miles (162 kilometers) from the tourist city of Oaxaca, according to the USGS.
For NDTV Updates, follow us on Twitter or join us on Facebook
