Fighting between the Jund al-Sham group and members of Palestinian President Mahmoud Abbas' Fatah movement on Monday began in the northern part of Ain al-Hilweh camp and quickly spread.
Sources said that the three killed were on Fatah's side. Several others were wounded and brought to hospitals in Sidon.
It was unclear what sparked the clashes, and each side blamed the other.
The Notorious camp
The impoverished Ain al-Hilweh camp, home to more than 100,000 refugees, has gained notoriety as a refuge for fugitives and for the settling of scores between factions.
The Lebanese army does not enter the camp under a tacit deal agreed after the 1975-1990 civil war. Palestinian factions are responsible for security.
The sound of fierce gunfire and rocket fire could be heard from neighbouring Sidon as clashes raged on Monday. The Lebanese army reinforced its positions at the four main entrances to Ain al-Hilweh.
"Ambulances have not been able to enter the camp because of the intensity of the fighting, and because they're happening near the camp's entrances," one Palestinian source inside the camp told the AFP news agency, speaking on condition of anonymity.
More than 450,000 Palestinians are registered in Lebanon with the United Nations Relief and Works Agency for Palestinian refugees.
Source: Bloom Gist, Al Jazeera
