Ambassador Mohamed Alhakim told reporters that in the last few weeks, bodies with surgical incisions and missing kidneys or other body parts have been found in shallow mass graves.
"We have bodies. Come and examine them," he said. "It is clear they are missing certain parts."
He also said a dozen doctors have been "executed" in Mosul for refusing to participate in organ harvesting.
Alhakim briefed the council on the overall situation in Iraq and accused Islamic State of "crimes of genocide" in targeting certain ethnic groups.
The outgoing U.N. envoy to Iraq, Nikolay Mladenov, told the council that in January alone, 790 people were killed in acts of terrorism and armed conflict.
Mladenov noted the increasing number of reports and allegations that Islamic State is using organ harvesting as a financing method, but he said only that "it's very clear that the tactics ISIL is using expand by the day." He used an acronym for the group.
He said Iraq's most pressing goal is to win back the vast territory that Islamic State has seized in the last year. The Sunni militants have seized about a third of both Iraq and neighboring Syria and imposed strict Sharia law.
"Especially worrying is the increasing number of reports of revenge attacks committed particularly against members of the Sunni community in areas liberated from ISIL control," Mladenov said.