At least 14 children have died, and several others are in a critical condition in hospital after the tragedy in the village of San Guiliano di Puglia.
Two women were also killed when nearby buildings fell on them.
More than 30 children and teachers have been pulled from the rubble alive but about 15 are still believed to be trapped inside.
After nightfall, teams guided by flashlights and floodlights rescued six dust-covered children from the rubble and sent them to nearby hospitals.
The children have confirmed that at least some of their classmates were alive.
The BBC's Brian Barron, reporting from the scene, says there is a tense atmosphere with parents and relatives clearly nervous and distraught, amidst fears that the building might collapse entirely.
Prime Minister Silvio Berlusconi has gone to the quake site to oversee the rescue efforts, after his government declared a state of emergency ensuring that funding was swiftly available as well as army participation in the rescue and recovery operations.
Many other buildings in the Campobasso area have collapsed and about 3,000 people are spending the night in emergency tents.
Distressed relatives
The remoteness of the area has hampered the rescue operation and a series of lesser quakes throughout the afternoon has meant they could not use large earth-moving equipment in their delicate task.
Rescue workers with lights, specially trained dogs and sonar equipment, are still struggling to shift the concrete.
Paramedic Antonio Licursi said he believed at least another dozen children were still trapped inside.
"The children continue to talk to us. They are in two different groups in two 'pockets', some of them are hiding under benches," a rescue worker said.
The roof of the school collapsed when the quake - which measured 5.4 on the Richter scale - struck at 1140 local time (1040 GMT).
The town of Campobasso suffered structural damage, as did five other villages.
Thousands of people rushed out on to the streets of Campobasso as cracks gaped in walls and chunks of plaster fell from ceilings, according to Italian news reports.
"I could feel the earth literally moving under my feet," said Gianfranco Di Ruta, a bar owner in the town.
"The lamps were swinging from the buildings. People were in shock."
A major highway bridge has been damaged, a railway line has also been closed after a viaduct was damaged, and many power and phone lines have been put out of action.
Recent Italian earthquakes
1997 - 13 die and 40,000 homeless as roof of Assisi basilica collapses
1980 - 2,500 killed and 7,500 injured in Naples
The BBC's David Willey says this is the biggest earthquake to hit Italy for several years.
He says Italy's civil protection agency, set up after the last earthquake in 1980, has swung into action fairly efficiently this time, and the emergency services are responding fully to this new disaster.
Seismologists had already been monitoring the region after this week's eruption of Mount Etna in Sicily, Europe's biggest active volcano.
A quake also hit Mount Etna on Thursday, measuring 3.7 on the Richter scale. It did not appear to be connected with the tremor hitting southern Italy.