The warplane was downed near the international airport of Aleppo, said the Syrian Observatory for Human Rights.
One of the pilots was found dead while the other couldnt be found yet.
This comes as intense battles were raging Saturday after the Syrian army captured the Tariq al-Bab neighborhood, which enabled it to secure a road toward the airport.
Meanwhile, pan-Arab al-Mayadeen TV said the Syrian air force were heavily striking the rebel positions on the road in a bid to secure it.
Flights to Aleppos airport have for long been halted out of fears of rebel attacks on flights coming or leaving the airport. Still, the airport was used as a military base only, Xinhua reported.
With the fresh advance, the Syrian army has become in control of nearly 60 percent of the rebel-held areas in eastern Aleppo, as part of a broad offensive the government forces unleashed to drive the rebels out of that key city.
The Observatory said 300 people have been killed in eastern Aleppo since mid-November. It added that 59 civilians were also killed as a result of the rebel shelling on government-controlled areas in the western part of the city.
Meanwhile, civilians continued to flee eastern Aleppo toward government-controlled areas as a result of the military showdown.
The International Committee of the Red Cross (ICRC) said recently over 30,000 people evacuated eastern Aleppo toward government areas over the past few days.
In a statement, the ICRC said the civilians must be guaranteed protection and safe passage.
"We appeal to all sides to ensure this. We at the ICRC are ready to help, but it is up to those who are involved in the fighting to protect civilians," it added.
The Syrian army says it will press on with the operation until all rebel-held areas in eastern Aleppo are recaptured. The rebels captured eastern Aleppo in 2012, and the government forces recently imposed a siege on that area before unleashing a broad offensive for its recapture.
Humanitarian organizations sounded the alarm about the situation of 250,000 people living in eastern Aleppo, with the government promising to fix the situation of those relocated in government-controlled areas.