One official said the attack was linked to a deadly row on July 20 in the camp, in which three Palestinians were killed, including Shehade Jawhar of Jund al-Sham, a predominantly Lebanese group, which associates itself more closely with the ideology of al-Qaeda.
"It was a retaliation for the assassination of Shehade Jawhar," he said. Jawhar is wanted by Lebanese authorities for murder.
After news of Tuesday's explosion spread, Fatah group fighters exchanged fire with Jund al-Sham fighters.
Ain el-Helweh has in recent months become the site of clashes between the rival groups.
Palestinian refugee camps in Lebanon are outside the control of the Lebanese authorities, with Palestinian factions, including Fatah, in charge of security.