The temblor's epicenter was about 280 kilometers west of Athens, near the town of Lixouri on the island, and its depth was 17 kilometers, the Athens Geodynamic Institute said.
A local news website, kefaloniapress.Gr, reported some damage on roads and buildings in the towns of Lixouri and Argostoli, the island's largest. There have been some slight injuries from falls, and falling objects inside apartments.
Local media reported several rock falls as well as damage to the local airport's control tower.
"It is too early to say if this is the main earthquake, although it likely is," Manolis Skordilis, an associate professor of geophysics at the University of Thessaloniki, told The Associated Press.
More From This Section
"This area shows the highest incidence of seismic phenomena, not only in Greece, but on an east-west axis stretching from Gibraltar to China. In 1983, there was a 7 magnitude quake in the same area ... We have already had many aftershocks and expect many more."
Costas Papazahos, a seismology professor at the same university, said the 5.8 was a preliminary reading, adding that he expects the final figure to be between 6 and 6.2 Such earthquakes are not rare in Greece. Kefalonia and the nearby island of Zakynthos were devastated by a 7.2-strong quake in 1953.