According to reports, there was an exchange of fire following a dispute outside a near-by hair salon.
The stray bullet hit the woman who was transferred to Attikon hospital, where she receives treatment.
There is no information yet on how serious the injuries are.
Police have launched a manhunt for the perpetrator.
In early June, an 11-year-old boy was killed by a stray bullet while he was playing in a school playground in the district of Menidi.
A 23-year-old Roma was arrested after having confessed that he fired a shotgun.