Enrique Rebsamen, a four-storey private school for primary and secondary age children, was reduced to rubble after the 7.1 magnitude quake tore through the capital Mexico City on Tuesday afternoon.
Frantic parents and locals took to social media to call for help as well as building equipment to free those trapped in the wreckage.
And hundreds of soldiers and police officers swooped on the scene, desperately digging through the rubble in the hope of finding pupils and staff still alive.
About 400 children are understood to attend the school.
Two children were rescued, but Mexican President Enrique Pena Nieto last night confirmed at least 20 had died in the collapse.
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Two teachers had also been killed – but officials say another 30 people are still missing.
Peña Nieto said on a video posted by his office to social media sites: “They are hauling out debris, material, trying to get through the rubble and rescue people.”
He pleaded with the parents for silence, saying: “You have heard some voices in the time that I’ve been here.”
Following the disaster, one woman took to Facebook to appeal for help locating her missing nephew.
A post being widely shared on social media reads: “Friends who are the south of Mexico City your help is needed, please!
“There are children beneath the rubble at the Enrique Rebsamen school.”
Reporter Julio Ibanez also tweeted footage of volunteers holding up handwritten signs with the names of children pulled from the wreckage.
He said: ”Please RT so that their parents known they’ve been found.”
The school’s collapse showed the devastating nature of the 7.4 magnitude earthquake, which struck on the anniversary of the 1985 earthquake which killed 10,000 people.
So far at least 220 people have been confirmed dead, according to Mexico’s interior ministry, but this could continue to rise.
President Pena Nieto said at least 27 buildings had collapsed in the capital after the quake struck at 1.15pm local time (7.15pm BST).
In a late night address, Mr Nieto said there are several reports of people trapped either beneath the rubble of collapsed buildings or inside burning ones.