The Ain el-Hilweh camp, on the outskirts of the southern coastal city of Sidon, has often seen factional disputes spiral into violence. Medical sources said the man killed was a civilian. Three other people, including a child, were wounded.
Gunmen from Fatah, the party of West Bank-based Palestinian President Mahmoud Abbas, have regularly clashed with Islamist militants in the camp, including supporters of Islamic State and al Qaeda.
Palestinian activists inside the camp urged people to protest against the violence, in which machineguns and rocket-propelled grenades have been used.
A loudspeaker on a mosque implored the warring sides to stop shooting to avoid civilian casualties, as gunfire rang out.
Shops and schools nearby closed as stray bullets landed in the area around the camp.
The latest wave of violence began on February 23. The UN Relief and Works Agency (UNRWA), which aids Palestinian refugees, said it had suspended all services in the camp on Monday and Tuesday because of the violence.
"There are reports of injuries to civilians and damage to shelters as a result of the weekend clashes," it said in a statement.
"An UNRWA installation is reported as sustaining minor damage and the unauthorised entry of armed actors into one UNRWA school was reported."
On a visit to Beirut last week, Abbas discussed with Lebanese officials the security arrangements in Palestinian camps in the country, which are home to nearly 450,000 Palestinian refugees.
Fatah has an agreement with Lebanese authorities to hand over wanted Islamist militants hiding out in Ain el-Hilweh, which is outside Lebanese security forces' jurisdiction, a security source said.
Attempted crackdowns by Fatah are a source of tension between it and the Islamists, the source added.