The 6.0 magnitude quake was centered about 8 miles northwest of the island’s capital of Argostoli.
Thousands of residents had been living with relatives or in ships dispatched for those who felt their homes were unsafe due to ongoing aftershocks.
Monday’s sharp aftershock hit before dawn at 5:08 a.m. local time at a depth of only 6,560 feet.
Shaking was felt across the western Greek mainland and as far away as Athens, 190 miles to the east.
Seismologist Vassilis Papazachos told reporters that Kefalonia residents should make plans for alternate shelter over the coming weeks or months if their homes are damaged.
Greek authorities have set up tents for islanders made homeless and brought in prefabricated classrooms so children can go back to school in safe structures.
The island has been visited by numerous destructive earthquakes throughout recorded history, including a 7.2 magnitude temblor in 1953 that struck three days after a 6.4 magnitude quake, killing hundreds and leveling nearly all of the buildings on Kefalonia and neighboring Zakinthos.