If confirmed, the presence of a Russian craft in the air space of the key NATO member would further ratchet up tensions over Moscow's behaviour in Syria. Russia denied it was to blame, despite repeated previous violations.
The Turkish army said that the craft had been warned three times by Turkish planes but had maintained course.
It was then "downed by fire from our aircraft on patrol, according to the rules of engagement."
The army warned the air force would "decisively" implement Turkey's rules of engagement.
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The US military believes the drone downed by Turkey was Russian, a US official said in Washington.
"All indications are, yes, it is a Russian drone," the official said, speaking on condition of anonymity. The official added there were no reports of the Syrian army using the type of drone that was shot down.
Television pictures showed the military examining the crash site by the village of Deliosman in the southern Kilis region on the Syrian border.
It appeared to be a drone used for reconnaissance operations.
Analysts said that the drone was similar to drones used by pro-Russian separatist forces in Ukraine, some of which had been shot down.
"A good working assumption is that it's Russian," said Nick de Larrinaga, Europe editor of IHS Jane's Defence Weekly, adding it was nonetheless different to a Russian Orlan 10 drone.