"He is not a fully fledged member and the group he has links to has not been identified.
"However, an Islamic group called Usbat al-Ansar has in the past been a cause for instability inside the camp."
The head of the Fatah armed wing in the camp told Al Jazeera's correspondent that the incident was isolated, that it was a fight between two men and was not political.
The Lebanese army cordoned off the main entrance to the camp outside the southern port of Sidon and dozens of families could be seen fleeing Ain al-Hilweh in fear, the AFP news agency said.
Some vehicles leaving the camp were transporting wounded people to nearby hospitals.
By longstanding convention, the Lebanese army does not enter the camps, leaving security inside in the hands of Palestinians.
Ain al-Hilweh, the largest of Lebanon's 12 Palestinian camps, is home to about 50,000 refugees.