The Britain-based Syrian Observatory for Human Rights said the crash occurred today in the northeastern city of Raqqa after five airstrikes hit the area.
A Raqqa-based activist who uses the name Fourat Alwfaa said the crash occurred after Islamic State fighters fired anti-aircraft weapons at the plane, but said it was unclear if the shooting had caused the crash.
The Observatory and Alwfaa said a family was killed after the plane crashed into their home.
Syrian officials rarely comment on such incidents.