The motive for the shooting was believed to be jealousy, and the shooter escaped and remained at large several hours later.
Police Lt. Col. Sujate Boonkong said the dead woman in the shooting at Century Plaza near Bangkok's Victory Monument was 28 years old.
The shooting came just over a week after a disgruntled soldier fatally shot 29 people in the northeastern city of Nakhon Ratchasima before being killed by security forces in the mall where he holed up for about 16 hours.
A masked gunman in January in the central Thai city of Lopburi killed three people and wounded four others in a mall while robbing a gold shop with a handgun fitted with a silencer. One of the dead was a 2-year-old boy. A school director was arrested less than two weeks later and reportedly confessed, saying he did not mean to shoot anyone.
Thailand has a high number of guns per capita held in civilian hands and a high number of gun deaths. The research team of Small Arms Survey estimated in 2018 that there are 15.14 civilian firearms per 100 people, the highest level in Southeast Asia.