The aircraft crashed in the mountainous region of Qalamun, northwest of the Syrian capital, the Britain-based monitoring group said.
"It is not known whether it crashed due to a technical fault or it was hit by rebels," Observatory head Rami Abdel Rahman told AFP.
The pilot ejected himself and landed near the town of Jayrud, 60 kilometres northeast of Damascus, he added.
Nusrat Al-Mazlum, a small group of Islamist rebels, captured the pilot and handed him over to another group, said Abdel Rahman, who was not able to identify the second group.
Jaish al-Islam's spokesman, Islam Alloush, posted a photo and a video of the pilot on his Twitter account, saying he belonged to the Alawite sect of President Bashar al-Assad.
Syria's official news agency SANA said the plane had crashed due to a "technical problem", adding that a search was underway for the pilot "who could have ejected and landed using his parachute".
Several government jets have been taken down by rebel fighters or crashed due to technical faults since Syria's civil war began five years ago.
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