The teen was shot in the O'Riada Court area of Ballymagroarty near a childrens playpark at around 11.15pm.
He was taken to hospital by a family member and police described his injuries as not life-threatening.
It's thought two men, wearing dark clothing, were involved in the incident.
Police have appealed for information.
It's the second such attack in Derry in the past four months; earlier this year a teenager was shot five times.
The 18-year-old was shot three times in his right leg, and two times in his left in the Creggan area in June.
Speaking from the scene, Cllr John Boyle said it was a barbaric attack: