"The National Institute of Anthropology and History (INAH) and the Oaxaca Institute of Cultural Heritage state in their latest report that 55 objects of cultural heritage were damaged in Oaxaca, the epicentre of the natural disaster", the ministry said in a statement.
Other refineries in the state are operating as normal, Mexican Oil said. Such a huge quake is classified as "major", and can cause serious damage.
Six hours following the quake, a lot more than 400 aftershocks had been recorded across the region, the strongest at 4.6 magnitude.
In February 2018, a magnitude 7.2 struck 225 km to the northwest of this event that injured four people and damaged 1,000 homes in Oaxaca.
The quake hit at 10:29 a.m. and the epicenter was located at 23 kilometers south of La Crucecita, a Pacific Coast village in southern Oaxaca state, the National Seismological Service (SSN) said via Twitter.
People remain outside buildings in Mexico City during a quake on Tuesday.
"The natural disaster also resulted in a tsunami threat message issued by NOAA's [National Oceanic and Atmospheric Administration] Pacific Tsunami Warning Center", USGS added in a news release.
"All those that are in an area with COVID patients remain inside, only those of us who weren't there at the time" have come out, said Jaime Gomez, a nurse at a hospital caring for coronavirus patients.
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