The earthquake has killed at least five people, with mass evacuations being organised, the Guardian reports.
It occurred 165km west of the state of Chiapas just before midnight on Thursday local time, and has been described as the strongest earthquake to hit the country since 1985.
Three people were confirmed dead in Chiapas, and two in Tabasco state, as the Pacific tsunami warning centre said waves as high as three metres could strike the coast.
Reports also suggested that a hotel in the south of the country was among the buildings that suffered severe damage, with rescuers searching for trapped people.
The FCO has so far not updated its advice for Mexico.