The United Nations warned at the end of May that up to 200,000 civilians may still be trapped in IS-held areas.
"The brutality of Daesh and other terrorist groups seemingly knows no bounds," said Zeid Ra'ad Al Hussein, using an Arabic acronym for IS.
"Yesterday, my staff reported to me that bodies of murdered Iraqi men, women and children still lay on the streets of the al-Shira neighbourhood of western Mosul, after at least 163 people were shot and killed by Daesh to prevent them from fleeing," he said in his opening address to the UN Human Rights Council.
"My staff have also received reports of missing people from this neighbourhood," he added, without providing further details.
His spokesman Rupert Colville told AFP that the killings were believed to have taken place on June 1.
IS seized Mosul in 2014, and the operation that began last October to retake the city has pushed hundreds of thousands of residents to flee their homes.
Iraqi forces have retaken all but a handful of areas around the Old City in western Mosul, but the jihadists are fighting in densely populated areas, and have used civilians as human shields at various points in the battle.
The United Nations warned at the end of May that up to 200,000 civilians may still be trapped in IS-held areas, facing shortages of food, water and medicine as well as deadly danger from the battle for the city.
Zeid on Tuesday condemned "in the strongest terms the cowardly and sickening attacks perpetrated against innocent people by callous terrorists operating in many parts of the world."