Police were alerted to gunshots in Rue Baudit just after midnight and found a woman seriously injured after being shot three times, Geneva's public prosecutor said in a statement. The victim was transported to Geneva university hospital (HUG) but died a few hours later.
The alleged perpetrator, a local resident born in 1977, was arrested at his home close to the crime scene.
An investigation has been opened to determine the circumstances surrounding the shooting.
Initial media reports suggested the alleged perpetrator may have been a friend of the victim, but others later said the pair didn't know each other but had simply argued over a small sum of money.
The public prosecutor will not comment further at this stage.