The temporary facility, which is in a stronghold of the rebel Houthi movement in northern Saada province, was struck on Friday.
It marked another deadly day in the war between Saudi led coalition forces and Houthi rebels which has been going on since 2015.
A spokesman for UN Secretary-General Antonio Guterres, Stephane Dujarric, said further deadly airstrikes had been reported elsewhere in Yemen with three children among those reportedly killed in the western city of Hodeidah.
“The Secretary-General calls for prompt, effective and transparent investigations into these incidents to ensure accountability.”
Meanwhile, the Houthi government’s health minister, Taha al Motawakel, described the airstrikes as a “war crime”.
“The coalition (Saudi-led coalition) is targeting civilians, they attacked the detention centre in Saada province that hosts civilian inmates known by the Red Cross and were visited by them, they were directly targeted by Saudi-led coalition aircraft. Until this moment rescuers are still searching for victims,” he said.
“We are looking at a very big crime and there is an American green light to kill civilians, that’s what we can see through targeting the detention centre in Saada province and the continuous killing of civilians without chasing the convicts or the war criminals.
“We consider this a war crime against humanity. The world should take its responsibility at this critical moment in human history, we are witnessing many victims.”
But the Saudi-led coalition said reports of it targeting the detention centre were untrue.
A coalition spokesman said the target in Saada was not on no-targeting lists agreed upon with the Office for the Coordination of Humanitarian Affairs, was not reported by the International Committee of the Red Cross and did not meet the standards specified by the Third Geneva Convention for Prisoners of War.
US Calls For De-escalation After Airstrikes
Meanwhile, the US Secretary of State, Antony Blinken, has called for a de-escalation in the conflict after the latest offensive.
On Friday, Mr Blinken said: “The escalation in fighting and attacks across Yemen must come to an end.
“We urge all parties to commit to a peaceful, diplomatic solution to ending the conflict. The Yemeni people deserve to live in peace and determine their own future.”
Years Of Fighting That ‘Needs To Stop’
Earlier this week, Houthis claimed responsibility for an attack on the United Arab Emirates, a member of the coalition, which killed at least three people and injured at least six others.
The Houthis said they fired four Quds cruise missiles at an oil refinery in the Musaffah district and airport in Abu Dhabi, a Zulfiqar ballistic missile at Dubai airport and several drones at those and other sites.
United Nations envoy for Yemen Hans Grundberg voiced grave concern over the military escalation and called on both sides to “exercise maximum restraint”.