The strongest of earthquakes, which began rumbling Wednesday, registered a magnitude of 6.2 and was in waters near the island in Tokyo's Izu island chain, Yomiuri Shimbun reported.
The earthquakes began Wednesday morning and extended into Thursday.
Although it is assumed the quakes are not related to any volcanic activity, the meteorological agency said it would monitor the situation.
The Oi nuclear power plant, Japan's only online nuclear reactor, is near the island, but its operator, Kansai Electric, said the earthquake didn't damage the facility.
Miyake village government officials said most damage, including landslides, was on the western half of the island.
Village officials and construction workers began clearing an earthquake-triggered landslide that inundated a road Thursday.
"We didn't expect this," a village official said. "We won't be able to open this road."