Oaxaca Gov. Alejandro Murat said at least two people died in his state, the epicenter of the 7.4 magnitude quake. Its epicenter was off the Pacific coast about seven miles southwest of Santa María Zapotitlán, near the beach resort of Huatuco.
Two people died in collapsed buildings, while another had a wall fall on him, said Gov. Alejandro Murat.
Gonzalez said there was some visible broken glass and mirrors, but no major damage.
The state of Oaxaca was central to the quake with sustained damage in many areas.
The epicenter was near Crucecita, in the southeastern state of Oaxaca, with shock waves felt as far away as Mexico City, some 700 kilometers (430 miles) distant, where it sent frightened residents rushing into the streets. Seismic alarms sounded mid-morning with enough warning for residents to exit buildings.
Helicopters hovered over downtown, and police patrols sounded their sirens.
A 7.4 magnitude quake hit Mexico's southern coastline yesterday, which lead to buildings getting collapsed and people getting evacuated.
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As many as 30 buildings in the capital were damaged, worldwide media reports said.
The Pacific Tsunami Warning Center said that hazardous tsunami waves may form within approximately 600 miles of the epicenter, including areas along the coasts of Mexico, Honduras, Guatemala, and El Salvador.
"This has the potential to be a deadly natural disaster and cause significant damage", US Geological Survey seismologist Paul Earle said.
Six hours after the quake, 447 aftershocks had been recorded across the region, the strongest at a magnitude of 4.6.
Medical staff and patients gathered outside Alvaro Obregon Hospital in Mexico City during the natural disaster. "It was strong, very strong", she said.
Early estimates from USGS of the earthquake's damage "suggest that localized casualties and damage are possible but there are likely to be fewer than 100 fatalities and less than $100 million in damage".
Mexico is located above various fault lines.