Officials did not confirm the group's claim to have shot down the jet as it struck their positions in the Qalamoun region on Wednesday.
In a statement via its official propaganda agency, the so-called Islamic State claimed a "Syrian regime warplane [was] shot down in East Qalamoun, north-east of Damascus".
Officials in Bashar al-Assad's defence ministry confirmed an aircraft had crashed but did not specify the cause.
A spokesperson said a pilot had been rescued after carrying out a combat mission against "Daesh terrorist groupings" in a rural area of Qalamoun.
It came days after a pilot was killed when Isis shot another Syrian Air Force plane down near the city of Deir Ezzor, which is split between jihadists and forces loyal to the President.
Local reports said the MIG-21 was downed using a 23mm anti-aircraft gun while targeting Isis positions at low altitude.
It was one of several attacks on Syrian jets claimed by jihadists, including an attack in July where they later hung a pilot's corpse on display in the streets.
Isis was not part of a fragile truce between the government and opposition rebels that ended on Monday evening.
The temporary ceasefire was marred by continued fighting and air strikes that struck a UN aid convoy, killing at least 12 people.
Syrian and Russian forces have denied responsibility for the bombing amid accusations from members of the US-led coalition, activists and monitoring groups.
President Assad’s government and supporters have also been angered by an operation by the US-led coalition that mistakenly killed dozens of Syrian regime troops while targeting Isis in Deir Ezzor.
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