The quake took place on Tuesday morning with the epicenter located 23 km south of La Crucecita, a seaside town along Oaxaca's Pacific Coast. The epicenter was 7 miles south-southwest of Santa Maria Zapotitlan.
"My condolences - at the moment, there are seven deaths in Oaxaca state", Governor Alejandro Murat said in an interview with Milenio TV.
The quake caused buildings in Mexico City to sway and sent thousands of residents into the city's streets Tuesday.
Tsunami waves are forecast to be less than 0.3 metres above the tide level for the coasts of Costa Rica, Ecuador, El Salvador, Guatemala, Hawaii, Honduras, Nicaragua, Panama, and Peru.
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Mexico City is particularly vulnerable to earthquakes mainly because its really tender and damp ground amplifies shaking and is inclined to liquefaction, in which grime transforms into a dense liquid when adequately churned.
There was no damage reported to "strategic infrastructure" including ports, airports, refineries and hydroelectric plants, President Andres Manuel Lopez Obrador said in a video published on social media.
Six hours following the quake, a lot more than 400 aftershocks had been recorded across the region, the strongest at 4.6 magnitude. "It was strong, very strong", she said. Smaller waves were expected through Central America, Peru and Ecuador. This has the potential to be a deadly natural disaster and cause significant damage, U.S. Geological Survey seismologist Paul Earle said.
Because oceanic crust is relatively dense, when the Pacific Ocean floor encounters the lighter continental crust of the Mexican landmass, the ocean floor is subducted beneath the North American plate creating the deep Middle American trench along Mexico's southern coast.
Earlier estimates put the magnitude of the tremor at 7.7, but it was revised down to 7.4 on the Richter scale.