In a statement on Twitter, Ahrar al-Sham, a hardline Islamist group that fights alongside Al-Qaeda's local affiliate, said it "shot down a warplane (over the town of Al-Eis) that was conducting airstrikes".
Earlier, a rebel source had confirmed that a regime warplane had been shot down, but said it was likely by fighters from Al-Qaeda's Syrian branch, Al-Nusra Front.
The source said the pilot had been taken alive.
The Syrian pro-government website Al-Masdar News identified the captured pilot as Khaled Said, quoting army sources.
It also reported, citing the same unnamed sources, the "death" of co-pilot Musaab Hourani, without giving further details.
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There was no immediate confirmation from the Syrian government or the armed forces.
Video footage circulating on social media purported to show the scene where the plane came down, with a dozen men crowding around a man lying in the dirt.
Some of them cry: "He's Syrian, he's Syrian!" and others yell: "Get his weapons off him!"
AFP could not confirm the authenticity of the footage.
Last month, Islamist rebels shot down a regime warplane over the village of Kafr Nabuda in the central province of Hama.
Ahrar al-Sham is allied with Al-Nusra across swathes of northern and northwest Syria, in a coalition called the "Army of Conquest."
On Friday, Al-Nusra and its allies pushed regime loyalists out of Al-Eis, a strategic town in Aleppo province.