One of the wounded was said to be in a critical condition.
Reuters earlier on Sunday reported that the clashes were between the Jund al-Sham, a Palestinian Islamist group, and supporters of Lebanon's Popular Nasserist Group in the southern Ain el-Hilweh camp.
But Aljazeera's correspondent in Lebanon said there was no Palestinian involvement in the fighting.
At least a dozen cars were set ablaze in the skirmishes after a personal dispute on Saturday in which one of the Nasserist group supporters stabbed a Jund al-Sham member, Reuters reported.
Armed groups sporadically clash over authority inside the tense camp, which the Lebanese army does not enter.
Aljazeera's correspondent in Lebanon, Abbas Nasir, said fighting had come to an end on Sunday evening in the al-Taamir area near the refugee camp.
At least a dozen cars were set
ablaze in Sunday's fighting
Nasir said that the clashes involved two Lebanese factions and that if Palestinian armed men were at the scene, they were independent of any Palestinian faction.
Khalid Arif, the secretary general for the Palestine Liberation Organisation in southern Lebanon, told Aljazeera: "What happened was a personal misunderstanding between some families who are located in al-Taamir district, but the Palestinian national and Islamic factions have nothing to do with the conflict."
He said government officials were trying to end the conflict.
"The Lebanese army command and the Palestinian-Lebanese national follow-up committee have intervened to resolve the conflict while an envoy was sent by Bahiya al-Hariri and Dr Usama Saad to help resolve the dispute," Arif said.
A Lebanese army checkpoint near the site of the fighting did not interfere, witnesses said.
About 390,000 Palestinian refugees live in 12 impoverished camps across Lebanon.
A UN Security Council resolution last year that led to the withdrawal of Syrian troops from Lebanon also demanded the disarming of Lebanese and Palestinian armed groups, most of them backed by Damascus.