A tsunami warning was initially issued, but later lifted. There are no reports of major damage or casualties.
The Japan Meteorological Agency gave the strength as 6.9 while the US Geological Survey put it at 7.3.
Japan is often hit by earthquakes. In 1995, a magnitude-7.2 quake in the port city of Kobe killed 6,400 people.
The latest tremor occurred at 0531 on Saturday (2031 GMT on Friday).
BBC News website reader Ivan Brackin, who lives on Yoron Island, said it was the biggest quake he had felt in his 40 years in Japan but there had been no visible effects in his area.
"We're 30 yards [metres] from the sea and no sign of a tsunami," he said.
"I woke up to violent shudders that lasted about six seconds then a pause followed by a couple of sharp jumps. Jumpers are the most dangerous so that sent me under the desk."