The source said the blast killed Fathi Zeidan, who headed the Fatah movement in the Miye Miye Palestinian refugee camp near Sidon.
"His identification card was found near the car which exploded, which was also his," the source told AFP.
A statement from Lebanon's armed forces said Zeidan had been driving the car when one kilogram of explosives hidden inside his vehicle detonated.
The army's forensics unit arrived at the scene of the blast and cleared away scorched body parts lying near a car in flames, according to an AFP correspondent at the scene.
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More than 450,000 Palestinians are registered in Lebanon with the UN agency for Palestinian refugees, and many live in squalid conditions in 12 official camps.
The camps are administered by Palestinian officials and security forces, rather than the Lebanese authorities.
In recent years, tensions have risen between Palestinian president Mahmud Abbas' Fatah movement and the Jund al-Sham Islamist group, especially in the Ain al-Hilweh camp, which is also near Sidon.
The rival factions in Ain al-Hilweh have clashed several times in the past year, with each side accusing each other of assassination attempts.
Ain al-Hilweh has become the scene of score-settling between several factions, and a breeding ground for extremist groups that have flourished on the back of the poverty afflicting the camp.