The incident occurred in Moadamiyeh, about five kilometres west of the Syrian capital and close to a military airport.
The Damascus correspondent for the pan-Arab al-Arabiya TV, whose offices are located close to the crash area, said employees did not hear the crash.
He said the aeroplane was "very quickly" taken away from the scene.
The crash comes amid tensions over a September 6 air raid by Israel which struck Syria close to the Turkish border.
Bashar al-Assad, the Syrian president, said late last week that the raid struck an unused military building. Israel has not said what the target was.