Since the initial quake, several strong aftershocks have shaken the region, including a magnitude 5.1. So far, there are no reports of deaths or injuries.
The quake hit at 11:02 a.m. PT., centered near Ometepec, about 200 miles south of Mexico City. The U.S. Geological Survey initially said the earthquake was a magnitude 7.6, but it was later downgraded.
In Mexico City, thousands of people evacuated their apartments and offices, and over one of the main streets, a bridge collapsed and crushed a van. Fortunately, no one was in the vehicle at the time. Telephone service was down in the city and through most of the area where the quake was felt.
Caltech seismologist Kate Hutton said the earthquake was shallow - about 11 miles below the surface. She said the earthquake occurred in what's called a subduction zone, where one plate of crust in thrust against another, but the temblor did not prompt a tsunami warning, Hutton said.
"These types of geologic structures actually create the largest earthquakes that we experience on the globe," said Robert Graves, a U.S.G.S. geophysicist.
So far, seismologists have not received much data from the area, and they say that indicates that power and phone service is likely down in the area. They expect aftershocks to go on for several weeks.
"Generally, the larger the earthquake, the more aftershocks and the longer the time period where they have significant ones," Hutton said.
David Munoz of World Vision in Mexico City said the shaking was so strong, that he fell to the ground.
"When I was able to reach the exit of the building, the cars on the streets were hitting each other because of the magnitude of the earthquake," Munoz said.
President Barack Obama's oldest daughter, Malia, was in Oaxaca on vacation with a school group at the time. The first lady's communications director said Malia Obama is safe and was never in any danger.
New Jersey resident Dan Reese was vacationing in Acapulco when the earthquake struck.
"Everything was shaking, people came running out of the building. I can't see any damage from here, but there's definitely sirens in the background and things going on," he said.
Tuesday's earthquake was one of the strongest to shake Mexico since 1985, when an 8.0-magnitude quake devastated Mexico City, destroying thousands of buildings and killing at least 10,000 people.
At LAX, travelers said they called home to check on family after news of the strong earthquake. Newlywed Michael Khalifa, who lives in Mexico City, got off his connecting flight from a honeymoon in Bora Bora to hear the news. He said he remembers the 1985 earthquake.
"I'm very afraid because my family is there, my job. I'm a civil engineer so I have a lot of buildings, and I want to know what happened," he said.
The Associated Press contributed to this report.