News agency Nepalnews said the protesters were rounded up into police vans and taken away from the scene, and that no one was injured. International media put the number of arrests at between 70 and 100.
Nepal, home to around 20,000 exiles from neighboring Tibet, has seen a series of protests since China's crackdown on pro-independence rallies earlier this month in Tibet's capital, Lhasa. Nepal, wary of angering its vital economic partner, has staunchly supported Beijing's position that Tibet is an inseparable part of China.
The agency said the demonstrators chanted slogans against China's 'genocide' in Tibet, and the deaths of 130 innocent protesters last week in Lhasa. Beijing puts the death toll at 20, and accuses Tibetan rioters of killing "innocent Chinese".
Tuesday's arrests come a day after a series of protests in Nepal, in which 475 demonstrators were reportedly detained, sparking condemnation from the United Nations.
The Nepal branch of the UN Office of The High Commissioner for Human Rights said: "These actions by police violate individuals' basic rights to freedom from arbitrary detention and freedom of movement, in addition to impairing the individuals' rights to peaceful assembly and expression.... A Government cannot suppress demonstrations merely on the basis of disagreement with the political opinions expressed."
Protesters also reportedly gathered on Tuesday outside the Kathmandu office of Chinese state news agency Xinhua. Nepalnews said the protest sites fall into "the restricted zone where all kinds of protests and demonstrations have been prohibited."
Law enforcement agencies said the detainees would be freed this evening.
China has accused Tibetan spiritual leader the Dalai Lama of orchestrating the Lhasa protests, which began on March 10 to mark the 49th anniversary of a failed uprising against Chinese rule.
The Dalai Lama, who lives in exile in north India, has dismissed the allegation, and voiced concern that that many people rounded up in mass-arrests following the Tibet protests could face harsh reprisals and even execution as Beijing seeks to stamp out dissent.