The attack took place early today as the interim leader was returning home.
However, one of the bullets penetrated the windscreen of the prime minister’s car, but he and his driver escaped unhurt.
Libya’s chief prosecutor has launched an investigation into the attack.
Meanwhile, the attack comes amid intense factional wrangling over the control of the government, with Dbeibah – who was named interim leader last year – pledging to fight efforts by his opponents to replace him.
Libya parliament members are scheduled to pick a new interim leader from between two candidates: powerful former interior minister Fathi Bashagha, 59, and outsider Khaled al-Bibass, 51, a former official in the interior ministry.