Mexico City: At least five people are dead after a strong magnitude 8.1 earthquake struck off the southern coast of Mexico, shaking buildings in the capital city and spurring tsunami warnings for waves up to three metres high.

People in Mexico City ran out into the streets after the quake struck at about 11.49pm, local time, as power went out in some neighbourhoods.

In the the suburb of La Roma, dozens of people stared at their phones in the dark to get news, while videos posted to social media showed power poles and monuments swaying as the earthquake struck.

At least three people in the southern state of Chiapas were killed, including two women who were crushed when buildings crumbled, said the state's governor Manuel Velasquez.