"Mitiga airport has been targeted by fire this morning, the first day of Eid al-Adha", the airport's management said in a statement on Facebook, referring to the three-day Muslim holiday that began on Sunday.
Air traffic was suspended "until further notice", the statement added, alongside photos showing columns of smoke rising from the runway and parked planes.
Haftar launched an offensive to take Libya's capital in early April, but encountered stiff resistance, resulting in months of stalemate in southern Tripoli's outskirts.
His self-styled Libyan National Army (LNA) and the Tripoli-based Government of National Accord (GNA) had on Saturday agreed to a UN-sponsored humanitarian truce for Eid Al-Adha, although the GNA had listed conditions, including a cessation of troop movements.
Late Sunday a joint statement from the United Arab Emirates, the United States, France, Italy and the UK welcomed the UN truce for the Muslim holiday and said they were "ready to assist the UN mission in monitoring the observance of the truce and address any attempt to break it."
But the GNA blamed Haftar's forces for the attack against the airport, and for a separate alleged attack in the Soug al-Jomaa district of Tripoli.
"Haftar's militias have violated the truce twice," GNA spokesman Mustafa al-Mejii told AFP.
"The first time targeted a home in Soug al-Jomaa, wounding three civilians, and the second hit Mitiga airport," he added.
Located east of Tripoli, Mitiga is a former military airbase that has been used by civilian traffic since Tripoli's international airport suffered severe damage during fighting in 2014.
Mitiga is in a zone under the control of forces loyal to the UN-recognised GNA and has often been targeted.
"We have noted the coordinates of the rocket fire from zones controlled by Haftar's militias south of the capital" and passed them on to the UN mission in Libya (UNSMIL), Mejii said.
Libyan TV channels also reported exchanges of fire around the road to the closed international airport on Sunday.
The truce had come after UN envoy Ghassan Salame had already called several times for humanitarian ceasefires, without success.
The joint statement from the five countries urged the parties to use the truce to "pave the way for a sustainable ceasefire and a return to a constructive, inclusive dialogue" towards a "lasting political solution."
Over the past four months, 1,093 people have been killed in the fighting and 5,752 wounded, according to the World Health Organization (WHO), while more than 120,000 people have been displaced.
Libya has been mired in chaos since a NATO-backed uprising that toppled and killed dictator Muammer Gaddafi in 2011.