The quake hit at 03:36 (01:36 GMT), 76 km (47 miles) southeast of the city of Perugia, at the very shallow depth of 10km (six miles).
The mayor of one town told Italian radio that "half the town is gone".
In Rome, some buildings shook for 20 seconds, according to La Repubblica newspaper.
Amatrice's mayor Sergio Perozzi told state-run RAI radio that the town had been badly damaged.
"The roads in and out of town are cut off. Half the town is gone. There are people under the rubble...
There's been a landslide and a bridge might collapse," he said.
Italy's Civil Protection agency described the earthquake as "severe".