A resolution passed by the top UN rights body demands that Moscow "cease the unlawful forced transfer and deportation of civilians and other protected persons within Ukraine or to the Russian Federation".
Highlighting the transfer of "children, including those from institutional care, unaccompanied children and separated children", the resolution was passed with 28 of the 47 council members voting in favour, 17 abstaining and only China and Eritrea opposing.
The Kremlin's alleged deportation of tens of thousands of children from war-ravaged Ukraine to Russia or areas occupied by its forces has been a hot topic throughout the nearly six-week session of the council in Geneva.
Kyiv maintains that more than 16,000 Ukrainian children have been deported to Russia as of February this year.
"The scope and brutality of Russia's atrocities in Ukraine are simply beyond any human comprehension," Ukrainian ambassador Yevheniia Filipenko told the council.
"The most appalling of them is the forcible transfer … of children to Russia for their re-education and adoption."
US ambassador Michele Taylor said: "The forcible transport, transfer and deportation of Ukraine's children is truly sickening."
But China pushed the resolution to a vote, with envoy Li Xiaomei condemning the text as an "instrumentalisation of human rights issues".
Ms Li insisted the council would have been better off supporting "dialogue between Russia and Ukraine" and should "stop spreading oil over fire".
Tuesday's resolution, which also prolonged for another year a high-level investigation into breaches committed in the context of the war in Ukraine, demanded that Russia provide access to all those transferred.
It said Moscow should grant "staff of established international human rights and humanitarian mechanisms unhindered, immediate, sustained and safe access" to those transferred.
And it called for Russia to provide "reliable and comprehensive information about the number and the whereabouts of these civilians, and ensure their dignified treatment and their safe return".
The text also called for "unhindered, immediate and sustained access" to be granted to all prisoners of war and anyone "unlawfully detained".
The high-level Commission of Inquiry , established by the council a year ago to investigate abuses since Moscow's full-scale invasion of Ukraine in February 2022, concluded in its first report last month that the forced transfers of Ukrainian children amounted to a war crime.
The investigators, who with Tuesday's vote have been given another year to push ahead with their work, said they were also inquiring into allegations that those transfers could amount to genocide.
And they highlighted other Russian offences in Ukraine which they said amounted to war crimes, including killings, torture and rape.
They warned that systematic attacks on Ukraine's energy infrastructure and a pattern of widespread and systematic torture could amount to crimes against humanity.
A day after the commission published its report, the International Criminal Court issued an arrest warrant for Russian President Vladimir Putin on the war crime accusation of unlawfully deporting Ukrainian children.
Amid a long line of resolutions passed on the last day of its main annual session, the UN rights council also agreed on Tuesday to appoint Bulgarian human rights expert Mariana Katzarova to monitor the situation inside Russia.
The move came after the council last September decided a special rapporteur was needed for Russia, amid concerns over an intensifying domestic crackdown by Moscow as its war rages in Ukraine.