Zeid Raad Al Hussein condemned "the repeated failure" of the coalition to prevent deadly incidents.
He said air strikes had caused almost all the coalition's civilian casualties.
More than 6,000 people, about half of them civilians, have been killed since Saudi Arabia launched a multi-national campaign against rebels in March 2015.
Saudi Arabia has denied causing large-scale civilian deaths, saying it is making every effort to avoid hitting civilian targets.
Mr Hussein's comments come three days after some 106 civilians were killed in what medics and witnesses said was an air strike on a market in Mastaba, north-west Yemen, in one of the deadliest incidents of the war.
The UN said staff who had visited the scene of the attack said, apart from a check-point about 250 metres (820 ft) away, there was no evidence it was a military target.
"Looking at the figures, it would seem that the coalition is responsible for twice as many civilian casualties as all other forces put together, virtually all as a result of air strikes," Mr Hussein said.
"They have hit markets, hospitals, clinics, schools, factories, wedding parties - and hundreds of private residences in villages, towns and cities including the capital, Sanaa."
"Despite plenty of international demarches, these awful incidents continue to occur with unacceptable regularity."
Saudi Arabia said it was investigating the attack on Mastaba, adding its forces had targeted a "gathering area" for Houthi rebel fighters about six miles (10km) away.
Zeid Raad Al Hussein however said coalition forces appeared not to have taken proper steps to distinguish between military and civilian targets, adding both they and the rebels might have committed "international crimes".
On Wednesday, Saudi Arabia's chief military spokesman, Brig Gen Ahmad al-Assiri, said the military campaign was "in the end of the major combat phase".
The coalition launched its offensive last March with the aim of repelling the rebels and restoring exiled President Abdrabbuh Mansour Hadi to power.