The 30-year-old was caught in crossfire that was the result of a dispute between two men.
The victim was taken to hospital where her condition was described as “stable”.
No arrests have yet been made but police are hunting thetwo men who made off separately from the scene.
A Metropolitan Police spokesman said: “Police were called at around 17:15 GMT on Sunday to Bournemouth Road, close to Rye Lane, following reports of shots fired.
“The woman was an innocent victim who was hit by a shot fired during a dispute between two men.”
The spokesman said that officers from the Met’s Trident command, responsible for tackling gang violence and preventing shootings, were investigating the incident.
Anyone who witnessed the shooting, or has information which could help the police, is asked to call the Trident South shootings team on 020 8785 8580 or Crimestoppers anonymously on 0800 555 111.
