Ischia Mayor Enzo Ferrandino called the incident a tragedy, according to media reports.
"The number of missing people in Casamicciola is still unknown. Due to the bad weather conditions, we have other critical situations, but not so acute," Ferrandino was quoted as saying by the news agency.
"There are eight people dead in the Ischia landslide. Rescuers are working in difficult conditions," Infrastructure minister Matteo Salvini said in a statement as quoted by local media.
Matteo Piantedosi, Italy's interior minister, was quoted by the media as saying that there were no confirmed deaths at the moment. The minister was visiting emergency services helping to coordinate the rescue, adding that the situation was evolving.
Meanwhile, other media reported that at least 13 people, among them one baby, had gone missing on Ischia as a result of the landslide caused by heavy rains. Several residential buildings, including a house with a family of three and a 25-year-old woman, were buried under the landslide.
Firefighters, civil defense officers and Italian carabinieri are now reportedly working at the scene of the incident. They have already rescued a man who got into a mudflow, media said.
A dangerous situation is also observed in another town, Lacco Ameno, where mudflows destroyed around 10 buildings and trapped roughly 20-30 people in their houses, the broadcaster reported, citing city Mayor Giacomo Pascale.
Italian Prime Minister Giorgia Meloni is in constant contact with the government of Campania, the region where the tragedy took place, and the civil defense service, the Chigi Palace said.
According to local authorities, 120 millimeters (4.7 inches) of rain fell on Ischia on Friday. Mudflows flooded the streets, damaged many buildings and cars.