Al-Maqdah was killed in a strike on a car, said Fathi Abu al-Aradat, a senior Lebanon-based member of the group that rivals Gaza’s Palestinian rulers Hamas.
A Lebanese security source and Lebanon’s official National News Agency reported the same information.
An AFP correspondent at the site of the attack said a car was struck near the Palestinian refugee camps of Ain al-Helweh and Mieh Mieh, adding that rescuers had pulled a body from the charred vehicle.
Dozens of angry Fatah supporters gathered inside the Ain al-Helweh camp, the AFP correspondent said, adding gunshots were fired in the air.