"Syrian air defences brought down a hostile US surveillance aircraft over north Latakia," the official SANA news agency said in a breaking news alert.
The agency gave no further details on the incident.
It appeared to be the first time Damascus had engaged an American aircraft in its airspace since a US-led coalition fighting the Islamic State group began strikes on Syrian territory in September 2014.
Syria is not participating in the US-led strikes against the jihadist group, but has so far refrained from taking action against the aircraft involved in the coalition's operations.
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The coalition's strikes in Syria have largely been focused on Aleppo and Raqa provinces, where the Islamic State has strongholds.
But it has also targeted the group elsewhere, and hit positions believed to belong to fighters affiliated with Al-Nusra Front, the Syrian wing of the Sunni jihadist Al-Qaeda.
IS fighters have been largely absent from the northwestern province of Latakia, according to the Syrian Observatory for Human Rights, a Britain-based monitor.