The failure to seek justice for victims was "contributing to the continuing horror", Zeid Ra’ad al-Hussein said, BBC wrote.
His comments came after the release of a report that said almost every rule of modern warfare was being flouted.
It found that civilians were targeted in airstrikes, prohibited weapons used and children recruited as soldiers.
The UN said at least 5,144 civilians have been killed — a quarter of them children — since March 2015, when a Saudi-led coalition began its war against Yemen.
The conflict has also left 20.7 million people in need of some kind of humanitarian assistance, created the largest food security emergency in the world, and led to a cholera outbreak that is believed to have affected 600,000 people since April.
The new report published in Geneva on Tuesday found that human rights violations and abuses were continuing unabated in Yemen, with civilians suffering deeply the consequences of an "entirely manmade catastrophe".
In many cases, it states, information obtained by UN officials suggested that civilians "may have been directly targeted, or that operations were conducted heedless of their impact on civilians without regard to the principles of distinction, proportionality and precautions in attack". In some cases, it appeared that "no actions were taken to mitigate the impact of operations on civilians."
Saudi-led coalition airstrikes — supported by the United States and United Kingdom — continued to be the leading cause of the 13,893 civilian casualties documented, reportedly killing 3,233 people.
The strikes targeted markets, hospitals, schools, residential areas and infrastructure, as well as funeral gatherings and civilian boats, the report said.
There was no immediate comment from the coalition, but it has repeatedly denied that its airstrikes have intentionally targeted civilians.