The earthquake, which measured 6.8 on the Richter Scale at its epicentre in Greece, was felt in parts of Puglia, Calabria and Sicily, particularly in the city of Catania, Giornale di Sicilia reported.
Residents in those areas reported feeling the tremors at around 8:10am. They had been given prior warning about the earthquake.
The epicentre of the quake was in Lefkada, a Greek island nestled between Corfu and Cefalonia.
A 59-year-old woman died when her house collapsed after being hit by a rock in the village of Ponti, Reuters reported, citing police. Several other buildings were also damaged, the news agency said.
Another woman is also reported to have been killed, although police have not confirmed the death.
The earthquake's magnitude was initially reported by the US Geological Survey as 6.7, and measured at 10km below the Earth's surface. A second reading revised the magnitude to 6.8, with a depth of only 5km.
Tremors and low-level earthquakes are often reported in Italy, though it is rare for quakes to cause damage. A series of earthquakes in the Emilia-Romagna region in 2012 killed 25 people, and in 2009 an earthquake in L'Aquila killed 308. Seven Italian scientists were convicted of manslaughter for failing to predict the seriousness of the L'Aquila quake, though these convictions were overturned in an appeal.
Several Twitter users claimed to have felt the tremors, while others said they had slept through.
Questa volta l'ho sentito il terremoto.— Cristina (@8dcdcd2890074f7) November 17, 2015
"This time I felt the earthquake"
Allora era un terremoto quello che ho sentito stamattina a #Catania, e io che avevo incolpato il dopo sbornia!
"So it was an earthquake that I felt this morning, and I blamed my hangover!"