The teenagers, most of whom were wearing school uniforms, carried "Free Tibet" placards as they entered the compound.
A U.N. spokesman told British media (BBC) the students apologized for entering the compound and said they wanted to draw attention to the crisis in Tibet.
Police today also arrested at least 60 other demonstrators who protested outside the U.N. facility.
Tibetan exiles have held protests in Kathmandu nearly every day for the past two weeks. Nepalese riot police have dispersed the rallies with baton charges and arrested hundreds of demonstrators.
Nepal officially supports Beijing's "One China" policy, considering Tibet and Taiwan part of China, and the home ministry has said it will not tolerate protests against what it describes as "friendly countries."
The U.S.-based Human Rights Watch says police are detaining monks and other Tibetans as they try to move around the capital, even when they are not engaged in protest.
The group also has called for Nepal to end the arbitrary detentions, threats and harassment of Tibetans in Nepal, and condemned excessive force used by police.
Some information for this report was provided by AFP, AP and Reuters.