Ticino cantonal police said the man, a 54-year-old Macedonian citizen living in Locarno, fired a gun at a 38-year-old Macedonian woman near the entrance to a supermarket multistorey car park at around 9am.
The woman died on the spot.
The man then attempted to take his own life. Injured, he was taken to hospital by helicopter. His life is not thought to be in danger.
Police said the pair were married and going through a separation. No other people were involved.