A police spokesman on the worst-hit island of Genkai said military and police personnel were checking the extent of the damage while searching for anyone who could be buried under collapsed buildings.
More than 100 aftershocks were felt after Sunday's earthquake, which measured 7.0 on the Richter scale. The meteorological agency warned on Monday that strong tremors measuring up to 6.0 on the scale could occur.
Most of Genkai's 750-strong population have been evacuated to Fukuoka, a large city on the island of Kyushu. In and around Fukuoka, nearly 2800 people have also fled their homes, a Municipal official said.
The quake occurred just before 11am (0153 GMT) on Sunday, damaging more than 600 houses, opening up cracks in 62 roads and triggering 11 landslides in the southern Kyushu region, including Genkai Island, according to police.
A 75-year-old woman was crushed to death under a wall, while at least 206 people were injured mostly by shards from shattered window panes and falling objects, police said. The Japanese media, however, said more than 400 people received treatment at hospitals for injuries.
The Meteorological Agency immediately issued tsunami warnings after the quake, but they were lifted an hour later after no rise in sea-levels was detected.
Experts said a tsunami did not occur because the fault was caused by the crust's horizontal shift rather than a vertical movement.
People have been alerted against
The earthquake's epicentre was located in waters 20km (13 miles) off Fukuoka, with its hypocenter 9km below the surface.
Police on Monday urged people remaining on Genkai Island to be alert for landslides.
"We need to be careful as it is forecast to rain tomorrow," the police spokesman said.
Tremors were also felt in South Korea on Sunday. Residents were forced to evacuate buildings in Busan, a key port city 50kms (280 miles) south of Seoul, the South Korean Yonhap news agency said. There were no reports of injuries or damage.
Sunday's quake was the biggest to hit Japan since a magnitude-6.8 quake rattled the Niigata region, about 200km north of Tokyo on 23 October last year, leaving 40 people dead.
The Niigata disaster was the deadliest in quake-prone Japan since 17 January 1995, when 6433 people died after a pre-dawn tremor in the western port city of Kobe.