The Iran-backed militia has been forcing neighbourhood leaders in Sanaa to recruit civilians, who are being taught to handle guns and sent to fight.
The UN agency said it had no choice but to reduce food aid as it is facing a 'severe' lack of funding in a 'very difficult' operating environment.
A Houthi-run court in Sanaa sentenced four journalists to death and is refusing to release another six who already served out their sentences.
'We are shocked that the Iranian authorities have once again defied their international obligations by executing a child offender,' UN experts said.
Yemen's Deputy Minister of Human Rights Nabil Abdul Hafeez described the Houthis' threat to the UN agency as 'cheap blackmail'.
Authorities at several prisons responded to protests with live ammunition and tear gas, killing some 35 inmates, rights group reports.
International aid organisations have been forced to reduce aid to Houthi-controlled areas due to the militia's corrupt handling of food relief.
The UN rights office said it was 'particularly shocked' as prisoner's death sentence was upheld despite being prohibited by international law.
Rights groups welcome the lifting of a death sentence handed down to a Bahai prisoner of conscience, saying the trial was a farce.
The Iran-backed militia's violations include executions, torture, forced disappearances, child recruitment and looting of public and private property.