Police arrested a 25-year-old Turkish man held responsible for the shooting but only after he shot several rounds into the air in front of the home where the attack took place, the ATS news service reported.
The dead man was the father of the separated wife of the man arrested, René Gsell, spokesman for the Basel prosecutor’s office told ATS.
The other victims were the wife, aged 31, and her mother, aged 58.
They were taken to hospital for treatment of serious injuries.
The entire family is of Turkish origin, according to cantonal police.
The suspect reportedly arrived at the home of his wife, where her parents were visiting at around 1pm.
A dispute broke out and the husband fired on the family members with a handgun.
Officers arrested him a short time later.
Police have launched an investigation into the case.