It is unclear if the killed soldiers were part of the Kurdish forces or if they are linked to the Syrian regime.
Syrian regime soldiers have been deployed in Kurdish-controlled areas as part of a deal to halt Turkish offensives against Kurdish forces.
Syria's government has not commented on the airstrike, but the pro-government Sham radio channel said a Turkish drone attacked a Syrian military post and that several Syrian soldiers were "martyred and injured".
The airstrike followed clashes that flared overnight between Turkish soldiers and the Syrian Democratic Forces (SDF), which is dominated by the Kurdish YPG militia.
Turkey's Ministry of Defense states that Kurdish forces then attacked on Turkish soil and killed a Turkish soldier, and that "13 terrorists" were killed in retaliatory attacks.