The MiG-23 went down after being targeted by "extremist militias", said a commanding officer with Haftar's forces.
The pilot ejected himself and survived unharmed, he said.
A source at the Benghazi airbase told the LANA news -which is linked to Haftar - that a "heat-seeking missile" had hit the plane.
Haftar has managed to retake a large part of the eastern coastal city of Benghazi from jihadi forces since it came under their control in 2014.
But violent clashes have been ongoing for several weeks between his forces and militants surrounded in their last bastions, especially in the area of Qanfuda south-west of the city.
Among the militias is the Revolutionary Shura Council of Benghazi, an alliance of Islamist militias that includes the al-Qaeda-linked Ansar al-Sharia.
Benghazi was the cradle of the 2011 uprising that toppled and killed longtime dictator Moamer Ghaddafi.
Libya has since fallen into chaos, with a UN-backed unity government failing to assert its authority over the country.
The parliament based in the eastern city of Tobruk has refused to recognise the Tripoli-based Government of National Accord.