The victim was walking on a residential street close to the university hospital HUG at around 11pm on Monday night when she was attacked, reported 24 Heures.
Hit several times on the head with an iron bar, she died at the scene from her injuries.
Speaking to newspaper 24 Heures, a man who lives in the neighbourhood said: “I saw the body on the ground and the paramedics trying to revive her as I walked home just after 11pm.”
Paramedics spent 45 minutes trying to save her, he said.
The victim was an Italian national from Turin who was in Geneva to pursue a doctorate in medicine at the university, said 24 Heures.
One of her professors confirmed her death to the paper.
“We have very little information but we are very much in shock and extremely sad,” he said.
According to the paper, the victim was just a few metres from her home when she was attacked.
The perpetrator, believed to be known to the victim, is thought to be a man of African origin, aged between 20 to 30 years old and about 1.90m tall.
The public prosecutor has opened a murder investigation and is appealing for witnesses to catch the man, who is still at large.
Anyone with information should contact police on 022 427 7240.