The 4.5 magnitude quake hit the tourist hotspot at 8:57pm local time (7:57pm UK time), according to Italian authorities.
Several buildings crumbled, including the island’s historic church, while the Rizzoli Hospital was evacuated.
At least 25 other people were injured in the quake while seven remain unaccounted for, local media have reported.
Locals and tourists ran out onto the street as the earthquake triggered a short electrical blackout across the island.
National newspaper Il Messaggero reported: “An inhabited building collapsed in Maio Square due to the effects of the earthquake.
“The Church of Purgatory has been destroyed, many hotels are isolated. There are several injured and some are missing.
“Police and firefighters are operating, as well as medical rescue units.”
Italian news agency ANSA added: “A shock magnitude 3.6 earthquake was recorded at 20:57pm in front of Ischia Island.
“People poured into the street while an electric blackout was in the centre of Ischia port. There is no damage to person or things.
“Ischia firefighters sent the rescue team to Casamicciola for a critical situation that was reported after the shock.”
Campi Flegrei, one of Europe’s biggest supervolcano, lies just nine miles from Naples.
Scientists from University College London (UCL) and the Vesuvius Observatory in Naples recently warned the volcano “may be approaching a critical stage”.
Dr Christopher Kilburn, director of the UCL Hazard Centre, warned officials that “further unrest will increase the possibility of an eruption”.
Professor Giuseppe De Natale, who also worked on the study, added: “We must adapt our preparations for another emergency, whether or not it leads to an eruption.”