The clash erupted in the Miyeh Miyeh camp near the main southern coastal city of Sidon at about 1 am (2200 GMT Wednesday) and raged for about 90 minutes before calm was restored, a Palestinian source said.
Palestinian president Mahmud Abbas's secular Fatah faction has been in open conflict with Hamas since the Islamist movement's violent takeover of the Gaza Strip in June.
The fighting broke out over a dispute between a Hamas militant and a Fatah rival over electricity supplies to a sector of the camp, the source said.
"It was an isolated incident that was rapidly brought under control," said Munir Maqdah, the Palestine Liberation Organisation's official in southern Lebanon.
"We don't want the events of Gaza to happen in the Lebanese camps."
Abu Mahmud, a Hamas official in Miyeh Miyeh, accused Fatah of "provocation" saying its supporters had ripped up posters of the late Hamas leader Sheikh Ahmed Yassin and his successor Abdel Aziz Rantissi, who were both assassinated by Israel.
The two injured men, who suffered bullet wounds, were identifed as a Fatah militant and a Lebanese who lives next to the camp.
After the events at the Nahr al-Bared camp, the Lebanese are in no mood to continue hosting Palestinian refugees if the camps are going to break out into open civil war.