It was the strongest expression yet of the anti-Iranian sentiment of Iraqi demonstrators, who have taken to the streets for weeks in Baghdad and the Shi'ite Muslim-majority south - and have been gunned down in their hundreds by Iraqi security forces.
Staff at the consulate had evacuated shortly before demonstrators broke in, police and civil defense first responders said. There were no immediate reports of casualties.
Local authorities imposed a curfew following the incident, state media reported.
The protests that began in Baghdad on Oct. 1 and have spread through southern cities are the most complex challenge facing the Shi'ite-dominated ruling class that has controlled state institutions and patronage networks since the 2003 U.S.-led invasion that toppled Sunni dictator Saddam Hussein.
Young, mostly Shi'ite protesters say politicians are corrupt, beholden to foreign powers - especially Iran - and blame them for a failure to recover from years of conflict despite relative calm since the defeat of Islamic State in 2017.