Kathmandu chief administrator Laxmi Dhakal said the 24 have been imprisoned for three months under the Public Security Act.
They have been charged variously with disturbing law and order, defying the administration's prohibition on protests and trying to damage Nepal's relations "with a friendly neighbor."
Three of those jailed are among 15 Tibetans arrested when they tried to storm the Chinese Embassy's visa office in Kathmandu on Wednesday.
The other 21 were arrested Thursday based on "information" they were leading anti-China activities in Nepal, Dhakal said.
This is the strictest action taken by Nepal so far against protesting Tibetans.
In the past, anti-China protesters had been kept in detention for a few hours and then freed.
"The Tibetans disturbed law and order, defied prohibitory orders, and attempted to damage Nepal's relations with China," Dhakal told Kyodo News. "As Kathmandu's chief administrator, I am authorized to jail such individuals for up to 90 days without trial."
Dhakal's office issued orders Monday prohibiting protests around the Chinese Embassy and its visa office.
Dhakal also summoned the Dalai Lama's representative Thinley Gyatso to his office and warned that anti-China protests would not be tolerated.
"We had requested them to observe the (51st anniversary of the Tibetan uprising against China) peacefully. They were adequately warned," Dhakal said.
Nepal has regularly detained Tibetans since they began protests targeting Chinese diplomatic offices in Kathmandu in March last year to decry the bloody Chinese crackdown on protesters in Lhasa, but the detentions had not been turned into prison sentences until now.
Nepal, home to more than 20,000 recognized Tibetan refugees and thousands more illegal Tibetan immigrants, is under increasing pressure from China to prevent the Tibetan community from organizing anti-China protests.
Nepal receives substantial development aid from China and officially considers Tibet part of China.