Mexico's interior minister and the governor of the south-west Oaxaca state were on board, but neither was hurt.
The aircraft's pilot lost control as it was coming in to land, Interior Minister Alfonso Navarrete said.
The 7.2-magnitude quake's epicentre was in Oaxaca but it shook buildings in Mexico City, 350km (217 miles) away.
No deaths have been reported in the earthquake itself.
A military helicopter carrying Mexico’s interior minister and the governor of the southern state of Oaxaca crashed on Friday killing two people during a tour of damage from an earthquake earlier in the day, but the senior officials survived.
Interior Minister Navarete told TV network Televisa that he and Oaxaca Governor Alejandro Murat were not seriously harmed in the accident that happened as the helicopter was attempting to land.
The ministry issued a statement on Twitter saying two people on the ground were killed when the helicopter came down.
The officials were surveying the aftermath of a 7.2 magnitude earthquake that rocked the rural state and Mexico City on Friday evening. The quake did not directly cause fatalities, but damaged dozens of buildings and knocked out power for a million people, authorities said.