Takayuki Ohigashi, 72, was found bleeding and unconscious in a parking lot in front of the company's headquarters in Kyoto at about 7:00 am, the Sankei Shimbun newspaper said.
He was later confirmed dead at hospital, public broadcaster NHK said.
He was bleeding from at least three wounds, suggesting he had been shot multiple times, reports said.
Ohigashi was president of the "Gyoza no Ohsho (King of Dumplings)" chain, operating more than 650 restaurants throughout Japan, as well as a handful abroad.