Hamas, which controls the Gaza Strip, is UNRWA's largest competitor, running a network of camps for roughly 100,000 children.
Groups with "misguided ideas"
There was no immediate claim of responsibility for Monday's attack.
Hamas condemned the raid and vowed to investigate. In a statement, the interior ministry blamed the attack on "groups led by those with misguided ideas who want to distort the situation in Gaza".
The Popular Front for the Liberation of Palestine also issued a statement condemning the attack.
The previous camp attack happened on May 23, when dozens of masked men tied up a night watchman, set fire to equipment and left a threatening letter for Ging.
The attacks have been widely attributed to extremist groups in Gaza that view the camps as religiously unacceptable, because boys and girls mingle freely.