The strike on the Al-Marja neighbourhood wounded several people, including at least one nurse, the civil defence, known as the White Helmets, said.
The clinic had been providing dental services and treatment for chronic illnesses for about five years.
Earlier this week, 30 people were killed -- including two doctors -- when air strikes hit the Al-Quds hospital and a nearby block of flats in the rebel-held Sukkari neighbourhood.
More than 200 civilians have been killed in Aleppo over the past week as rebels have pounded government-held neighbourhoods with rocket and artillery fire and the regime has hit rebel areas with air raids.
On Friday, air strikes on rebel-held districts killed two civilians, one of them a child, the Syrian Observatory for Human Rights said.