The earthquake, the strongest to hit Mexico since 1985, struck late on Thursday and people in Mexico City ran out into the streets.
At least two people were killed in the southern state of Chiapas, according to the interior minister.
Its epicentre was 123km southwest of the town of Pijijiapan, at a depth of 33km, according to USGS.
"The house moved like chewing gum and the light and internet went out momentarily," said Rodrigo Soberanes, who lives near San Cristobal de las Casas in Chiapas, a poor, largely indigenous state popular with tourists.
Chiapas Governor Manuel Velasco told television station Televisa the rooves of homes and a shopping center had collapsed in San Cristobal.
"There are damages in hospitals that have lost energy," he said. "Homes, schools and hospitals have been affected."
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Civil Defense in Chiapas said on its Twitter account that its personnel were in the streets aiding people and warned residents to prepare for aftershocks.
The quake was so powerful that frightened residents in Mexico's distant capital city fled apartment buildings, often in their pajamas, and gathered in groups in the street. Sections of Mexico City were without electricity.
The US Tsunami Warning System said widespread hazardous tsunami waves were possible within the next three hours on the Pacific coasts of several central American countries - Mexico, Guatemala, El Salvador, Costa Rica, Nicaragua, Panama, Honduras and Ecuador.
Lucy Jones, a seismologist in California who works with the U.S. Geological Survey, said such as quake was to be expected.
"Off the west coast of Mexico is what's called the subduction zone, the Pacific Plate is moving under the Mexican peninsula," she told Associated Press news agency.
"It's a very flat fault, so it's a place that has big earthquakes relatively often because of that."
"There's likely to be a small tsunami going to the southwest. It's not going to be coming up and affecting California or Hawaii," she said.