Contact with the jet was lost and the military is now searching for the pilot, who had ejected, the SANA news agency reported, citing a military source.
Turkish Prime Minister Binali Yildirim has confirmed that a Syrian military plane had crashed in south Turkey's Hatay province.
Media reports said, citing Turkish sources, that the jet was a MiG-23 fighter rather than a MiG-21.
Debris of a crashed Syrian fighter jet were found near the Turkish border with Syria, according to the Hatay province governor.
The pilot apparently had ejected, the governor added.
The news comes amid the nationwide ceasefire in Syria between Damascus and Syrian rebels that came into force on December 30, and has been holding up in general, despite continued reports of violations. The UN Security Council passed a resolution in December supporting the effort.