The Kyodo news agency says about 40 people are being treated at a hospital in Kumamoto, some of them seriously injured, and the government says at least 19 buildings have collapsed. At least two deaths occurred in the town of Mashiki, where the shaking was most severe. The town lies 15km east of Kumamoto.
The earthquake, which struck east of Kumamoto city at 9.26pm, and a second major quake, measuring 5.9, struck about midnight.
There was no tsunami warning, but Japan's chief government spokesman, Yoshihide Suga, said several buildings had collapsed. He gave no more details.
A fire also broke out in Mashiki, a town of about 34,000 people near the epicentre of the quake. NHK showed footage of firefighters tackling a blaze at a building.
Some 16,000 households in the area were without electricity and 38,000 homes had no gas supplies in Kumamoto, Japanese media reported.
After the first tremor, the Nuclear Regulation Authority said there were no irregularities at three nuclear plants on the southernmost island of Kyushu and nearby Shikoku.
Some high-speed trains were halted as a precaution.
A quake of magnitude 9 struck offshore north of Tokyo in March 2011, causing tsunami waves along the coast which killed nearly 20,000 people and triggered a meltdown at a nuclear power plant.