The temblor, which hit west of Kyushu Island at 10.53am (0153 GMT), was centred at an "extremely shallow" depth of 9km below the ocean floor, the Japanese Meteorological Agency said. Aftershocks followed - at least one a magnitude-4.2 quake.
Officials reported water and gas main breaks and power blackouts.
Local and bullet train railway service was halted, after an automatic safety mechanism was triggered by the tremors, public broadcaster NHK reported. Telephone service in the southern prefecture was jammed.
Minutes after the shaking began, the agency warned of the possibility of 50-centimetre tsunami waves triggered by the seismic activity and cautioned residents near the water to move to higher ground.
But an hour after the quake, the agency said there was no danger of tsunami. "There may be some disturbance of the ocean's surface, but we aren't worried about tsunami damage," said Masahiro Yamamoto of the Meteorological Agency.
Yamamoto predicted strong aftershocks measuring up to magnitude-6 would continue.
A 75-year-old woman, who was taken to hospital after a wall fell on her in southern Fukuoka city, became the first casualty of the quake, the Kyodo News agency said.
"There may be some disturbance of the ocean's surface, but we aren't worried about tsunami damage"
the Meteorological Agency
At least 250 people, most in hard-hit Fukuoka prefecture (state), were injured by the quake, some struck by toppling cabinets, items falling off shelves or shattered glass, and two were burned by a cooking stove, NHK said.
A prefectural government spokesman in Fukuoka, 899km southwest of Tokyo, said authorities had only confirmed 35 injuries, including 7 seriously.
In neighbouring Saga prefecture's Okawa city, a 56-year-old man suffered broken bones after trying to jump to safety from the second floor of his home, NHK said.
One person was reportedly rescued after being pinned inside a collapsed home.
"We have had frightened residents coming to the store because their own homes are shaking with every aftershock," said Shigeru Harada, a manager at convenience store Lawson in Fukuoka city.
Located along the Pacific Ocean's seismically active "Ring of Fire," Japan is one of the world's most earthquake-prone countries.
It is also one of the best prepared for a major quake. Tough requirements making buildings quake-safe and frequent disaster drills probably contributed to keep injuries and structural damage to a minimum in Sunday's temblor.
About 100 residents of Genkai, a tiny island off the coast of Kyushu, evacuated collapsed homes and other damaged buildings, and eight people were airlifted to hospitals on the main island of Kyushu, NHK said.
Prefectural officials requested help from Japanese troops, but landslides of topsoil and rocks loosened by the quake were hobbling emergency response efforts.
A Fukuoka prefectural police spokesman said the initial jolt, which lasted about 30 seconds, made it difficult to stand.
Last years' tsunami was triggered
by a 9.0-magnitude quake
NHK showed tall office buildings and street lamps in the centre of Fukuoka, nearest the epicentre, shaking violently. In residential areas, cracks appeared in sidewalks and parts of retaining walls flaked off.
Authorities warned of landslides around Fukuoka, Saga and Nagasaki prefectures. Kyushu Island is separated from South Korea by a narrow strait of water, and the quake was felt about 21km away in South Korea's port city of Busan, where it briefly shook buildings.
No damage was immediately reported, a police spokesman in Busan said.
A magnitude-7 quake can cause tremendous damage in populated areas, either directly or by triggering tsunami, which are distinguished from normal coastal surf by their great length and speed.
On 23 October, a magnitude-6.8 earthquake struck Niigata, northwest of Tokyo, killing 40 people and damaging more than 6000 homes.
The jolt was the deadliest to hit Japan since 1995, when a magnitude-7.3 quake killed 6433 people in the western city of Kobe.
On 26 December, a 9.0-magnitude quake triggered a massive tsunami that devastated Asian and African coastlines in nearly a dozen nations, killing at least 175,000 people.