The Libya Shield militia accused forces loyal to the internationally recognised government of carrying out the attack close to the Ras Jedir border crossing.
"One Libya Shield member was killed and between three and five were wounded," spokesman Hafedh Muammar told AFP.
Libya Shield forms part of the Islamist-backed militia alliance which seized the capital and much of the west in August, forcing the internationally backed government to take refuge in the remote east.
Tunisian defence ministry spokesman Belhassen Oueslati told AFP that the country's air space had not been violated in the raid but that air force patrols had been stepped up in the border region.
Forces loyal to the government have carried out a series of air strikes in western Libya in recent days, drawing condemnation from the UN mission to the North African country, which said it was undermining its efforts to broker an end to the unrest.
"The United Nations Support Mission in Libya (UNSMIL) condemns in the strongest terms the recent air raids and the escalation in violence in Libya," it said.
"UNSMIL also expresses deep concern at the negative effects the military escalation is having on the process of political dialogue."
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The UN mission announced on Wednesday that Special Representative Bernardino Leon will lead a new round of negotiations between the warring parties on December 9.
"The continuing escalation in the violence and statements threatening more military action do not help create the atmosphere conducive to hold this political dialogue." UNSMIL said.
On Thursday, forces loyal to the internationally recognised government hit what they said was a militia position in the south of Tripoli.
But their militia rivals, who have set up their own administration in the capital, said the strike hit a poultry farm.
On Tuesday, air strikes on the coastal city of Zuara, between Tripoli and Ras Jedir, killed seven people, including five African migrant workers.
Forces loyal to prominent former general Khalifa Haftar, who is now allied with the internationally recognised government, control the Al-Woutia air base in western Libya.
Haftar's forces have been battling Islamist militia in second city Benghazi since October. He has also vowed to end militia control of the capital within three months.
More than three years after dictator Moamer Kadhafi was toppled and killed in a NATO-backed revolt, Libya is awash with weapons and powerful militias, and has rival parliaments as well as governments.