The country's meteorological agency said the quake struck at 5:33 am (6:33 am AEST) near Awaji island in the Seto Inland Sea southwest of the city of Kobe at a relatively shallow depth of 10 kilometres.
The US Geological Survey measured the tremor at 6.0 but at an even shallower depth of five kilometres.
An 82-year-old woman in Fukui prefecture suffered a broken leg after she fell to the ground, while another woman, 74, in Hyogo prefecture broke her hip bone.
Japan's public broadcaster NHK showed footage of flattened brick walls and one house where all the roof tiles had collapsed to the ground.
Local train services were suspended for safety checks, while Kansai airport in Osaka Bay was temporarily closed.
Kansai Electric Power said there was nothing untoward at its Oi nuclear power plant, currently the only one in Japan with reactors online.
"Our operation has continued as we haven't monitored any abnormality, but we are still checking if there is any damage to the facilities," a plant official said.
Japan is regularly hit by powerful earthquakes and has largely adapted its infrastructure to tremors that can cause widespread damage in other, less developed countries.
Today's was the biggest to hit western Hyogo prefecture since 1995, when a 7.2-magnitude quake destroyed its port city of Kobe and killed more than 6,000 people.
Hikaru Doi, a 36-year-old employee of a taxi company on Awaji island, told Jiji Press: "I was scared to death. I thought a big quake hit again."
In March 2011, Japan suffered a massive undersea quake with a magnitude of 9.0, which sent a towering tsunami into the north-east of the country, devastating coastal communities and killing nearly 19,000 people.
It also sparked the world's worst atomic accident in a generation when waves knocked out the cooling systems at Fukushima nuclear plant.
Japan turned off its 50 reactors in the wake of the Fukushima disaster but the two at the Oi plant resumed operations due to fears of a power shortage.