Interior Minister Alfonso Navarrete told the Televisa network the pilot of the military helicopter lost control of the aircraft at a height of about 40 meters (130 feet) as it was coming in to land.
The natural disaster came less than six months after two quakes killed hundreds of people in the country.
A strong natural disaster shook a large swathe of southern and central Mexico on Friday, triggering the quake alarm system in Mexico City and causing buildings to sway.
Officials in affected states said they were already inspecting buildings damaged by last year's quakes, which are especially vulnerable to collapse. The country dealt with two back-to-back quakes in September that left hundreds dead after buildings crumbled, including schools.
Mexican President Enrique Peña Nieto tweeted that the quake was northeast of Pinotepa Nacional, in Oaxaca, and that "protocols have been activated". The epicentre was 24.6 km underground near the town of Pinotepa de Don Luis in Oaxaca state. After the natural disaster, 60 secondary quakes were recorded, with the strongest of magnitude 5.9, TASS reported.
The U.S. Geological Survey originally put the magnitude of Friday's quake at 7.5 but later lowered it to 7.2. The district is the site of numerous collapsed and badly damaged buildings from last year's temblor.
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Emergency warning systems were activated in Mexico City, some 348 kilometers (216 miles) from the centre of the quake, and many buildings were evacuated.
The powerful, sustained shaking on Friday gave way to 225 aftershocks, the national seismology service said, and caused widespread panic.
A total of 150 aftershocks were registered, the strongest of which had a magnitude of 5.9.
Maricarmen Trujillo was in the same place Friday on the eighth floor of a Mexico City office building where she rode out a September 19 quake that killed 228 people in the capital alone.
That quake knocked down buildings as far away as Mexico City and resulted in at least 9,500 deaths, 30,000 injured and 100,000 homeless.