Top government spokesman Yoshihide Suga confirmed the deaths of a child and a man, and said a third person was also feared dead in the quake.
Local police said the child who was killed was a nine-year-old girl who lived in the city of Takatsuki, north of Osaka, where a wall collapsed on her at school.
Japan's Fire and Disaster Management Agency said 41 others had been injured.
A building burns after the quake in Osaka.
Two elderly men and one 9-year-old girl died after being hit by collapsing walls and furniture, according to the Japan Times.
The quake, which was recorded at a depth of 13km, left more than 170,000 households without power in Osaka prefecture and neighbouring Hyogo prefecture, where an natural disaster killed more than 6,400 people in the city of Kobe in January 1995.
Alert: Heat Advisory is in effect for much of CNY Monday
As daytime heating kicks in again, storms will become likely by midday and last through the mid part of the afternoon. This stretch of heat shows little relief at night, especially in numerous urban areas, such as Chicago and NY .
Trump blasts Schumer for downplaying North Korea summit
Officials have not verified reports that North Korea may have demolished a stand used for missile-ejection tests in May. Recently, Park filmed a video op-ed imploring Trump to do the right thing when he meets Kim Jong Un .
European Central Bank gets ready to pull the plug on stimulus
All that money flooding into the financial system through banks pushed up the prices of investments likes stocks and bonds. Italian bond yields rose sharply this month as a new government of anti-establishment parties promised higher spending.
Around 170,000 houses in Osaka prefecture are experiencing power outages following the quake, NHK reported. "Almost all of the dishes fell and shattered on the floor", Kaori Iwakiri, a 50-year-old nurse in Moriguchi - just north of Osaka city - said. Centered inland from the port city, the quake did not cause a tsunami. There were no reports of abnormalities at its nuclear plants in the region.
Train and subway service including the bullet train that links Osaka to Tokyo was stopped have been suspended to check for damage to equipment.
In 1995, a 6.9 quake killed more than 6,000 people in Kobe, 30 kilometers to the west of Osaka.
Prime Minister Shinzo Abe told reporters the government was "working united, with its first priority on saving people's lives".
No irregularities were detected at the Mihama, Takahama and Ohi nuclear plants to the north of Osaka, Kansai Electric Power said.
Japanese Self-Defense Force fighter jets and helicopters are heading to the area to gather information.