The quake struck on Tuesday morning at about 06:00 local time (21:00 GMT, Monday), the Japan Meteorological Agency said.
The depth of the quake was estimated to be around 25km (15.5 miles). In 2011, a large tsunami caused by a quake destroyed the Fukushima nuclear power plant.
A tsunami warning was also issued for Miyagi prefecture, where a 1.4m wave (4.6ft) was observed at Sendai port.
The US Geological Survey initially put the magnitude at 7.3 but later downgraded this to 6.9, lower than the number given by the Japanese authorities.
Tokyo Electric Power has been checking the Fukushima plant for damage from the latest quake.
Cabinet Chief Secretary Yoshihide Suga told a televised news conference that the water cooling system on the third reactor of the Fukushima plant had stopped working, but there were no signs of temperatures rising and no other abnormalities at other nuclear facilities.
The plant operator later said it had restarted the cooling system.
All reactors in the Fukushima nuclear plant were shut down following the 2011 disaster, but cooling is still needed for the used nuclear fuel stored on the site.
Damage from the quake remains unclear, but there are some reports of minor injuries. Tremors were felt in Tokyo and residents were urged to evacuate some coastal areas.
Ships could be seen moving away from harbours in Fukushima prefecture.
So far, a wave of 60cm (2ft) has arrived in Onahama Port in Fukushima, Japanese broadcaster NHK reported, and another of 90cm in Soma. But the warning of possible larger waves remains in force.
Local media said the tsunami would hit repeatedly, and warned locals not to leave shelter until the warning was lifted.
Japan lies in a particularly seismically active region and accounts for around 20% of quakes worldwide of magnitude 6.0 or more.
At least 50 people died in two quakes in the southern Kumamoto prefecture in April.
More than 18,000 were killed or reported missing following the 2011 Fukushima disaster.