Masako Mori said she ordered the execution of Wei Wei "after careful consideration", over robbery and multiple murders carried out with two other students in 2003.
"It is an extremely cruel and brutal case in which the happily living family members, including an eight-year-old and 11-year-old, were all murdered because of truly selfish reasons," she said.
Wei, a 40-year-old former language student in Japan, had pleaded guilty to the four murder counts but had contended he was not a central figure in the case.
The trio, reportedly allured by money, robbed the home of Japanese businessman Shinjiro Matsumoto, 41, in southwestern city of Fukuoka in June 2003 and strangled him with a tie.
His 40-year-old wife Chika was drowned in a bathtub and the children strangled or smothered.
The victims' bodies were found dumped in Hakata Bay in Fukuoka, handcuffed and weighted down.
The other two suspects fled to China but were arrested there. One of the two was executed in 2005, according to Jiji Press, the year a Chinese court gave him a death sentence and his associate a life sentence.
According to the Asahi Shimbun daily, the first execution of a foreigner since the ministry began announcing the names of those executed was in 2009.
A Chinese man was hanged for killing three Chinese whom he lived with near Tokyo and for injuring three, the Asahi said.
Japan last executed inmates in August when two men were hanged after being convicted of murder.
Japan in 2018 hanged 15 inmates of which 13 people belonged to the Aum Shinrikyo cult that carried out the fatal 1995 sarin attack on the Tokyo subway and other crimes.
With more than 100 inmates on death row, Japan is one of few developed nations to retain the death penalty, and public support for it remains high despite international criticism, including from rights groups.