The fighting between the Jund al-Sham Islamist group and members of Palestinian President Mahmud Abbas's Fatah movement prompted hundreds of residents to flee Ain al-Helweh camp and shelter in nearby mosques.
Medical sources told AFP at least 35 people were wounded, with ambulances unable to enter the camp to retrieve more injured because of the intensity of the clashes.
At least two of the dead were Fatah members, one of them an officer, Palestinian sources said. The identity of the third person was unclear.
The Lebanese army reinforced its positions at the four main entrances to Ain al-Helweh.
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Soldiers were allowing those able to reach the entrances to leave the camp, but preventing anyone from entering, an AFP correspondent said.
At a mosque near the camp, some 900 people were sheltering after fleeing the violence, many of them Palestinians already displaced by the war in Syria.
The courtyard was filled with children playing games, while adults mostly sat inside.
A man who gave his name as Abu Khaled, originally from the Yarmuk refugee camp on the outskirts of Damascus, bemoaned the cramped conditions in the overwhelmed mosque.
"There are charities giving out bits of aid, but it isn't going to everyone," he said.
The clashes in Ain al-Helweh first broke out on Saturday after two Fatah members were killed during an apparent assassination attempt by Islamists on a leading Fatah official.
They continued sporadically throughout the weekend.