A 15-year-old also died on Friday after the clashes, which broke out in a southern suburb of Beirut, al-Manar television reported on Sunday.
The 11-year-old, Mohammed Hussein Naji, died from his injuries, two days after Lebanese police shot him in the head.
Naji's mother was shown on al-Manar TV wailing, she said: "I fled with him from one place to another to protect him during the Israeli war. But he was killed by the Lebanese state."
The city's southern districts are a stronghold of Hezbollah, the political party and Shia fighters' group that was targeted by Israel during its 34-day offensive in Lebanon in July and August.
However, the area where the riot took place on Friday was not among the hard-hit neighbourhoods, authorities said.
People there simply took advantage of the chaos and the government's preoccupation with the war and relief to build illegal housing, officials said.