Firefighters said the shooting occurred around 8am in the Geumam district in the nation's administrative capital.
The 50-year-old gunman, identified only by his surname Kang, opened fire with a shotgun in and outside the store, which was run by his former live-in partner, Sejong police chief Lee Ja Ha told reporters.
The woman's current boyfriend, father and brother, who was the store manager, were all shot and pronounced dead at hospital, Yonhap said.
The woman, who had not been present at the scene of the shooting, was taken into protective police custody for questioning.
"It was a pre-meditated crime caused by a combination of spurned affection and a row over how to divide property," Mr Lee said, adding that Kang and the woman had run the store together before they separated.
South Korea's tough gun control laws effectively outlaw ownership of firearms by most civilians.
Rare exceptions are allowed for hunters but they must store their rifles at local police stations.