The incident occurred shortly before 10am in the underground parking lot of a small apartment building where the victim lived in the community of 7,770 people, Le Matin newspaper reported.
The victim, who lived alone, was planning to help out one of his sons who has a kennel in a rural part of Geneva, the newspaper said.
He went to fetch his car and met a neighbour with whom he chatted for 20 minutes, Le Matin said, citing the neighbour.
Afterward, the neighbour heard a gunshot without any words exchanged and saw the victim “fall to the ground”.
The witness said he then ran to his apartment to call the authorities before hearing another detonation and returning to the parking area.
“The (female) shooter, dressed with elegance left in a confident way, without hurrying.”
The Geneva prosecutor's office, which is directing an investigation, is seeking a woman who knew her victim, Le Matin said.
Police arrived on the scene and cordoned off an area of the village until around 4pm, evacuating the perimeter between the municipality's two schools and the municipal hall.
The murder follows the suspected shooting of a woman on April 3rd by her husband in their home in the otherwise placid community, where almost a third of residents are expats.
Geneva police arrested a man born in 1973 in connection with the killing.