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.
Yemeni officials are calling on relief organisations to put alternative mechanisms in place to ensure aid reaches the targeted recipients.
There had been a recent escalation in harassment of journalists working for Persian news outlets outside Iran, coinciding with a crackdown on dissent within the country.
'Families of children killed during the protests are facing a ruthless campaign of harassment to intimidate them from speaking out,' spokesman says.
The judgement, one of a series passed against lawmakers and government ministers who oppose the militia, lacks legal basis, experts say.
The Iran-backed militia looted a World Food Programme warehouse, enriching themselves at the expense of Yemen's neediest women and children, officials say.
Yemen's Deputy Minister of Human Rights Nabil Abdul Hafeez says the Houthis are fully to blame for an expected cutback of assistance.