It cited lootings, property destruction, abductions and killings in territory recaptured from the Islamic State (IS) group.
Sunni Arabs face discrimination from Iraqi authorities and other groups who accuse them of supporting IS, it added.
In October, Amnesty International raised concerns over "war crimes" by Kurdish fighters in northern Syria.
The UN said it was particularly worried about 1,300 Sunnis stranded in "no-man's-land" near Sinjar, between Kurdish security forces and IS.
"Reports indicate that Iraqi security forces and Kurdish security forces and their respected affiliated militias have been responsible for looting and destruction of property belonging to Sunni Arab communities, forced evictions, abductions, illegal detention and, in some cases, extrajudicial killings," UN spokeswoman Cecile Pouilly said.
"We have received reports as well about their limited access to basic services and essential goods, such as water, food, shelter and medical care," she added.
Ms Pouilly said the UN had also received reports of 16 mass graves containing the bodies of those killed by IS - but added it was unclear how many bodies were in the graves.
Her office has called on Iraq's government to investigate, she told reporters.
Sinjar, in northern Iraq, was liberated from IS in mid-November. The militant group captured the town in 2014, killing and capturing thousands of Yazidis.
Sunni Arab communities left behind now face accusations of sympathy for IS, according to the UN.
The UN says it is "extremely concerned" by reports of attacks by Kurdish forces on Sunni Muslim Arabs living in Iraq.