Mexico President Enrique Pena Nieto said at least 27 buildings had collapsed in the capital after the earthquake struck.
Reports have emerged of people trapped beneath the rubble of collapsed buildings after the city was rocked at 1.15pm local time (7.15pm BST).
In the footage, a huge building can be seen shaking during the massive quake before it crumbles away.
People can be seen sprinting out of a building as the neighbouring block shakes before parts break away and crash to the floor.
Screams can be heard as what appears to be students and teachers can be seen quickly moving away from the building to safety.
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Smoke or dust can be seen rising into the air in the background as the building crashed away.
A Twitter user, who posted the video online, wrote: “Students and Teachers evacuating the Campus, horrific footage.”
The country’s President confirmed that 22 bodies had been recovered from a collapsed school in Mexico City where 38 people remain missing.
The governor of the neighbouring state of Morelos said at least 42 people had been killed there.
Mexican officials have said that the death toll so far is at least 248 people.
Many people fled into the streets, and electricity and phone lines were down in parts of the capital.
The earthquake comes just days after Mexico was hit by an 8.1 magnitude tremor, the biggest to hit Mexico in a century, killing at least 98 people.
The city and its surrounding area are home to about 20 million people.
The Mexican stock exchange suspended trading following the quake.
US President Donald Trump said on Twitter: “God bless the people of Mexico City. We are with you and will be there for you.”
The quake comes on the 32nd anniversary of a 1985 quake which killed 5,000 people and caused serious damage to the Greater Mexico City area.