The quake hit the same central regions that have been rocked by repeated tremors over the past two months.
The magnitude-6.6 earthquake caused extensive damage but no fatalities, despite registering much higher than the earthquake which stuck on August 24 and killed almost 300 people.
Weakened by repeated powerful jolts in recent weeks, many of Norcia's churches, monasteries and chapels were wrecked.
"We thought it was the end of everything," said 74-year-old Sister Maria Raffaella Buoso after being evacuated from the Monastery of the Poor Clares of Santa Maria della Pace.
The United States Geological Survey said the quake was centred 68 kilometres east-southeast of Perugia at a depth of 1.5 kilometres.
Geoscience Australia seismologist Hugh Glanville told the ABC that at that depth, the earthquake was very shallow and had the potential to cause anything nearby to be catastrophically damaged.
"If it's a deep earthquake at 10, 20 or even 30 kilometres, the seismic waves have to travel through more earth before they reach the surface, but at such a shallow depth there is a lot less to dampen the waves effect on the buildings," he said.
That there were no reports of fatalities was largely due to the fact that thousands had left their homes after the earlier temblors.
Some 20 people suffered minor injuries.
Premier Matteo Renzi pledged that wrecked homes, churches and businesses would rise again, saying they were part of Italy's national identity.
"We will rebuild everything," Mr Renzi said.
"We are dealing with marvellous territories, territories of beauty."
Norcia's historic Basilica of St Benedict was among the buildings destroyed.
The Monks of Norcia tweeted images of the damage and said people were trapped in the town's main square, with fears nearby buildings might collapse.
"Everyone has been suspended in a never-ending state of fear and stress. They are at their wits end," Bishop Renato Boccardo of Norcia said.
"It's as if the whole city fell down," Norcia city assessor Guiseppina Perla told the ANSA news agency.
The destruction of the Norcia basilica is the single most significant loss of Italy's artistic heritage in an earthquake since a tremor in 1997 caused the collapse of the ceiling of the Basilica of St Francis in Assisi.
The basilica and monastery complex dates to the 13th century, although shrines to St Benedict and his sister had been built there since the 8th century.
During his Sunday blessing Pope Francis offered his prayers to those affected.
"I'm praying for the injured and the families who have suffered the most damage, as well as for rescue and first-aid workers."
Department head Fabrizio Curcio said the agency was using helicopters to tend to the injured and assess damage.
'It's as if the whole city fell down'
Priests advised to hold outdoor mass
Cardinal Gualtiero Bassetti, head of the Catholic Bishops Conference of Umbria, advised parish priests not to hold mass inside churches.
He told priests in the Umbria region to hold mass outdoors, the ANSA news agency said.
The quake was felt as far north as Bolzano, near the border with Austria and as far south as the Puglia region at the southern tip of the Italian peninsula and was felt strongly in the capital Rome.
Marco Rinaldi, Mayor of quake-hit Ussita, north of Norcia, said a huge cloud of smoke erupted from the crumbled buildings.
"It's a disaster, a disaster," he told the ANSA news agency.
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