Dozens of Kenyans have been abducted in recent months, according to human rights groups, who blame the extrajudicial arrests on Kenya's police and intelligence services.
Kenyan authorities have said that the government does not condone or engage in extrajudicial killings or abductions.
Some groups of young protesters marched in downtown Nairobi while others staged a sit-in and chanted slogans against the government, with some holding placards denouncing illegal detentions, according to footage shown on the NTV broadcaster.
The national police spokesperson did not immediately respond to a request for comment on Monday's protests.
The alleged abductions followed anti-government protests that started in June this year.
Initially aimed at overturning proposed tax hikes, the demonstrations eventually evolved into a movement that cut across Kenya's traditional ethnic divisions, becoming the biggest threat to the incumbent President William Ruto's government.