The first attack struck a residential area, while the second hit a hospital shortly afterward, civil defense sources said, Anadolu Agency reported.
Video footage on social media showed casualties amid the ruins of the Al Shifa hospital.
Turkey's Anadolu agency also put the number of those killed at 13 and said 27 were injured. A local Turkish official said sources at the hospital claimed the Syrian Kurdish YPG militia hit the building with a missile launcher, according to initial reports.
The official said Turkish artillery is shelling rural positions near the city of Maarat al-Numan in response.
According to SANA, the incident was the result of shelling between Turkish forces and their backed militias on one side and the US-backed QSD militants on the other.
RHM/PR