It's the second such attack in as many months.
Hamas has launched an investigation into the previous incident. Elements in the Gaza Strip told Ynet that under the current situation only Hamas armed personnel have the ability to carry out such attacks.
There was no claim of responsibility.
However, Islamic extremists have accused the main UN aid agency of corrupting Gaza's youth with its summer program of games, sports and human rights lessons for some 250,000 children.
The UN's main competitor is the Islamic militant Hamas, which operates camps for some 100,000 children and offers lessons on Islam and military-style marching.
Local UN spokesman Adnan Abu Hasna says vandals broke into a camp site in central Gaza early Monday. He says they burned down tents and damaged facilities, but gave no further details.
Ali Waked contributed to this report