Zeid Raad Al Hussein said bodies were being found in buildings where IS had reportedly held people as human shields and were later targeted in air strikes.
He urged the coalition to avoid such "traps" and abide by international law.
Amnesty International has accused the coalition of failing to take adequate precautions to prevent civilian deaths.
The human rights group reported earlier on Tuesday that it had found evidence on the ground in Mosul pointing to an "alarming pattern" of air strikes that had "destroyed whole houses with entire families inside".
Coalition officials have so far not commented on the Amnesty report, but they have previously insisted they take all reasonable precautions to reduce the risk of harm to civilians.
Coalition forces have carried out hundreds of air strikes in the battle to recapture Mosul
Iraqi pro-government forces launched an offensive to recapture the city - the last major IS urban stronghold in the country - five months ago.
The coalition has supported the assault by carrying out hundreds of air strikes and by deploying military advisers and special forces personnel.
Although more than 286,000 civilians living in the city have fled their homes during the fighting, many more have followed the Iraqi government's repeated instructions to stay put until they are reached by troops.
Amnesty said the fact that residents were being told to remain at home meant the coalition had to know that air strikes were likely to result in civilian casualties.
Although thousands have fled their homes, many have followed advice to wait for troops
Any failure to take precautions to prevent civilian casualties would be "in flagrant violation of international humanitarian law", it warned.
According to information verified by the UN, at least 307 people were killed and another 273 injured between 17 February, when the government launched an assault on the western half of Mosul, and 22 March.
The deadliest incident occurred on 17 March, when an air strike - reportedly targeting IS snipers and equipment - hit a house in Jadida district.
Witnesses reported that IS had previously forced at least 140 civilians into the house to be used as human shields. They also said IS had booby-trapped the house with improvised explosive devices (IEDs).
Mr Zeid said that official figures so far indicated that at least 61 people were killed in the incident, but the actual figure may be much higher.
The coalition has launched an investigation into the incident, and the US military has said an initial review of data indicated that an air strike was carried out in the vicinity on that day.
However, the Iraqi military has said its experts inspected the site and found no evidence of an air strike. Instead, they saw the remains of a "huge, detonated booby-trapped vehicle".
The UN has also received numerous reports of IS snipers shooting at, and in some cases killing or wounding, civilians attempting to flee towards advancing troops, and also of IS shelling civilians in areas retaken by the government.
"[IS]'s strategy of using children, men and women to shield themselves from attack is cowardly and disgraceful. It breaches the most basic standards of human dignity and morality," said Mr Zeid.
"And shooting civilians in the back as they flee for their lives is an act of monstrous depravity."
But he stressed that conducting air strikes on IS locations in densely-populated areas, particularly given the clear indications that IS was using large numbers of civilians as human shields, might "potentially have a lethal and disproportionate impact on civilians".