Fighting between the Jund al-Sham extremist group and members of Palestinian President Mahmud Abbas's Fatah movement began in the northern part of Ain al-Hilweh camp and quickly spread, an AFP correspondent said.
Hospital sources in Sidon told AFP that two people were killed, including a Fatah officer. They did not confirm whether the second victim was a civilian or militant.
At least six people were wounded, a Palestinian source said.
Families of the wounded gathered at hospitals in Sidon to wait for news.
The sound of fierce gunfire and rocket fire could be heard from neighboring Sidon. The Lebanese army reinforced its positions at the four main entrances to Ain al-Hilweh.
The escalating standoff between radical groups and Fatah has erupted into clashes several times over the past few months.
On Saturday, two Fatah members were killed when extremists tried to murder a leading Fatah official.
It was unclear what sparked Monday's clashes, and each side blamed the other.
"We can confirm that there is a large number of wounded," one Palestinian source inside the camp told AFP, speaking on condition of anonymity.
"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," the source added.
An AFP correspondent said dozens of families fleeing the violence were heading into Sidon.
The impoverished Ain al-Hilweh camp has gained notoriety as a refuge for extremists and fugitives and for the settling of scores between factions.
By long-standing convention, the army does not enter the Palestinian refugee camps, leaving the factions themselves to handle security.
More than 450,000 Palestinians are registered in Lebanon with the United Nations Relief and Works Agency for Palestinian refugees.
Most live in squalid conditions in the country's 12 official refugee camps.