The consulate building in Najaf was torched and the Iranian flag was removed and replaced with an Iraqi one. Staffers inside were not harmed and escaped through a back door.
One protester was killed and 35 were wounded when police opened fire to prevent them from entering the facility. Protesters previously attacked an Iranian consulate in Karbala earlier this month. No one was harmed in that attack.
Wednesday's events marked an escalation in demonstrations that have raged for weeks across southern Iraq over dissatisfaction with public services, government corruption and high unemployment despite the country's oil wealth.
At least 350 people have been killed and thousands injured in what has become the largest grassroots movement against the government in Iraq's history. The unrest has become the country's biggest challenge since the defeat of the Islamic State terror group that took over vast swaths of territory several years ago.
Protesters occupying three bridges in central Baghdad -- Jumhuriya, Ahrar and Sinar -- in a standoff with security forces tried blocking authorities from accessing the areas.
Demonstrators across southern Iraq have burned tires and blocked access to roads leading to major oil fields in several provinces. Major roads to Umm Qasr and Khor al-Zubair ports were blocked on Wednesday, reducing trade activity by 50%, according to the port official.
In Karbala, five people were killed when authorities fired live rounds in an attempt to disperse crowds late Tuesday. In Baghdad, three simultaneous explosions rocked the city late Tuesday, killing five people and wounding more than a dozen.
The bombings occurred near Tahrir Square, the epicenter of Iraq's anti-government demonstrations.