"IS fighters fired on a military aircraft which crashed," the Britain-based group said.
"It is the first aircraft shot down since the regime launched air strikes against the jihadists in July following their declaration of a caliphate in late June," said the group, which relies on a wide network of doctors and activists for its reports.
Observatory director Rami Abdel Rahman told AFP that the plane was carrying out strikes on the IS stronghold of Raqa when it was hit.
A photograph posted on a jihadist Twitter account purported to show the burnt-out wreckage of the plane.
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"Allahu Akbar (God is greater), thanks to God we can confirm that a military aircraft has been shot down over Raqa," another account said, congratulating the "lions of the Islamic State."
The plane is far from the first Syrian government aircraft downed by opposition forces, but it comes after President Bashar al-Assad's regime stepped up its air campaign against IS in eastern Syria.
An air strike on an IS training camp in the Deir Ezzor town of Tibni killed 17 militants and a child on Saturday.
US President Barack Obama announced last week he had authorised the expansion to Syria of the air campaign against IS that he launched in neighbouring Iraq in early August.
There have been no US strikes in Syria so far but Obama's announcement, which was made in defiance of the Syrian government, drew protests from Damascus and its Iranian and Russian allies.
The fighting in Dakhaniya, near the eastern outskirts of Damascus, also killed 12 opposition fighters overnight, the Observatory said.