According to police, the incident occurred two hours after midnight in the center of Athens. The couple was in a car and had a fight for reasons as yet unknown.
The man shot the woman and afterwards threw her out of the car and fled. The perpetrator threw the gun in a dustbin a short distance away from the scene and disappeared.
The 20 year-old victim was taken to a hospital by ambulance.
Police are conducting an investigation to locate the perpetrator.