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 agency loyal to the parliament in Libya's east backed by 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 jihadists since it came under their control in 2014.
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These jihadist groups include 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 Kadhafi.
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.
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