The victim and the four wounded belonged to Fatah, a Lebanese security official said. There was no immediate word on casualties among Jund al-Sham fighters.
The echo of gunfire reverberated in Sidon and prompted hundreds of civilians in the teeming camp to flee to safer areas.
An AFP correspondent said more than 100 Palestinian families fled the camp to take refuge in nearby Sidon.
The correspondent added that entire families took refuge in a neighbouring mosque, while others hid in cars which they had managed to take out of the camp, home to about 45,000 people.
"There is a ceasefire ... the regrettable clashes that took place have ended" following mediation by another group, Mounir al Makdah, a Fatah official, said.
He said the Jund al-Sham fighters would leave the camp in the following hours and Fatah security agents would take control, with civilians which fled welcome to return on Saturday morning.
"There won't be a second Nahr al-Bared at Ein al-Hilweh," al Makdah said, referring to the three months of fighting between Lebanese army and Fatah al-Islam fighters that destroyed the Palestinian refugee camp in northern Lebanon.
A Lebanese army spokesman said that the fighting was confined to the camp and that troops, which by longstanding convention do not enter Lebanon's dozen refugee camps, had not got involved.
The Lebanese army blocked the entrance to the camp, while allowing civilians to leave.
The clashes were triggered after Fatah arrested Samir Maarouf, a member of Jund al-Sham, on Thursday and handed him over to the Lebanese army on charges of attempting to kill a Fatah official in the camp, Palestinian officials in Ein al-Hilweh said.
"Yesterday [Thursday] the Fatah organisation in the camp kidnapped a member of Jund al-Sham named Samir Maarouf who is accused of carrying out bomb attacks inside the camp and outside," a Palestinian official, who asked not to be identified, said.
"The Fatah forces handed over Maarouf to the Lebanese army," the official said, adding that the captive was suspected of links to armed groups outside Lebanon.
The report was confirmed by a Lebanese security official in Sidon.
In response to the arrest of their comrade, Jund al-Sham gunmen attacked Fatah offices in the camp with machine-gun fire and rocket-propelled grenades, the officials said.
Fatah fighters hit back with their own volleys of RPGs and machine-gun fire.
Jund al-Islam fought a deadly battle with Lebanese soldiers last year, joining in a revolt by fellow group of Fatah al-Islam centred on the north Lebanon refugee camp of Nahr al-Bared.
The group's name refers to the ancient Islamic term of Bilad al-Sham, a region which covers Syria, Lebanon, Jordan, Israel and the Palestinian territories.