Security forces in Karbala fired live ammunition to disperse protesters trying to scale the walls of the consulate in the southern city and torch it.
Journalists witnessed protesters left motionless after suffering gunshot wounds, and the forensic medicine department later confirmed three people died.
More than 250 people have lost their lives since anti-government rallies broke out in Iraq on 1 October, but officials have stopped providing casualty numbers.
In Karbala late on Sunday, protesters hung Iraqi flags on the concrete blocks surrounding the imposing Iranian consulate and spray-painted "Karbala is free, Iran out, out!" on them.
Others threw rocks or shot fireworks over the walls into the consulate, then set fire to tyres at the gates of the building as police officers looked on.
As the crowds grew, heavy gunfire and volleys of tear gas rang out.
"They're not firing up in the air. They intend to kill, not disperse," said one young protester wearing a medical mask to protect himself from the tear gas.
"They're protecting the Iranian embassy while all we want is a country. Why are they killing their own countrymen for another country?"
Iraq has close but complicated ties with its eastern neighbour Iran, with whom it fought a deadly war in the 1980s but which now has significant political and economic sway in Iraq.
Every year, millions of Iranian pilgrims travel to the holy city of Karbala, 100 kilometres (60 miles) south of Baghdad, to visit the golden-domed mausoleum of Hussein, the Prophet Mohammad's grandson.
But many Iraqis protesting over the past month accuse Iran of being the primary sponsor of the corrupt, inefficient system they want to overthrow.
Tehran, meanwhile, has sought to clamp down the protests next door, with sources reporting top commander Qassem Soleimani making several visits to "advise" Iraqi authorities on coping with the rallies.
Iran's Supreme Leader Ayatollah Ali Khamenei has also slammed protests in Iraq and Lebanon as conspiracies by the US and others.
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