"An argument escalated between members of the presidential guard.
The Tobruk lawmaker Saleh Hashem was lightly injured as he intervened to separate them," the witness said.
"A guard was also shot and wounded. They have both been admitted to hospital and are doing well," he added, speaking on condition of anonymity.
The witness did not detail the cause of the row outside parliament, which is located in the eastern city of Tobruk.
A 2015 UN-brokered deal that set up a Government of National Accord was meant to calm years of chaos that followed the ouster and killing of dictator Moamer Kadhafi in 2011.
But the Tripoli-based unity government struggled to win the support of the elected parliament in Tobruk and its legitimacy was questioned by its rivals from the very start.
Eight killed in suicide attack in eastern Libya: security officer
Sitting lawmakers were elected in 2014 and were due to vote at the end of July on a plans to organise a referendum on a Libyan constitution.
Parliamentary sessions have repeatedly been adjourned due to lawmakers arguing over the legal text and no further sessions are scheduled until the end of August.
Aguila Saleh Issa, the parliament speaker, was one of four Libyan leaders to commit in May to organising elections on December 10 in an agreement in Paris that sought to unite rival factions.
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