Rescuers are desperately trying to reach two brothers trapped under rubble after the quake brought down several buildings.
They pulled free the boys’ seven-month-old brother at around 04:00 local time, several hours after the tremor struck.
The island of Ischia, off the coast of Naples, has a population of about 50,000.
Ischia is extremely popular with tourists, many of whom were out in the bars and restaurants when the earthquake hit at 20:57 – striking at a depth of around 3 miles just north of the Casamicciola commune.
One elderly woman was reportedly killed by debris falling from a church, while another body was found in the rubble of collapsed building.
At least 1,500 people have been left homeless, Il Messagero reports.
The seven-month-old boy was rescued from a family home that collapsed, to cheers from the emergency workers.
The father and two women, one of whom is pregnant, were also saved from the rubble.
Now rescuers are trying to reach the baby’s two brothers. They have been given water by the emergency workers, local media reported.
Angelo Borrelli, head of civil protection, told was quoted by La Repubblica as saying they were cautiously optimistic of reaching the boys, but warned as “more time passes the more the situation becomes complicated”.
Parts of the island were said to be without power.
A hospital in another badly hit commune, Lacco Ameno, had to be evacuated. According to local media, the injured were treated outside the building and a number of patients were airlifted to Naples.
The Italian Red Cross confirmed on Twitter they were working with local authorities.
Extra ferries, from Naples to Ischia, were laid on during the night to bring more rescue workers to the island and allow holidaymakers to leave. Dozens of people are said to have ended their holidays early and Italian media said some tourists were sleeping on benches waiting for boats to arrive.
An emergency response team was quickly on the scene, partly because additional numbers were already on Ischia to fight localized bush fires.
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