It was not immediately clear who was responsible.
The Syrian Observatory for Human Rights quoted local residents as saying the plane was brought down by shooting from the Turkish side of the border. Al Manar, the television station of Lebanon's Hezbollah group, said two rockets were fired from Turkish territory.
But Turkish media quoted officials as denying Turkey had shot it down and said Syrian rebels were responsible.
(Reporting By Dominic Evans in Beirut and Daren Butler in Istanbul)