Local media reports indicated that at least one civilian was killed in the explosion, which occurred outside the heavily guarded consulate compound in the mostly Christian Ankawa district. The area is popular with foreigners and is home to many cafes, restaurants and hotels.
The Kurdish Rudaw website reported two civilians killed and at least eight injured in the bombing. Other accounts indicated that three people may have been killed in the blast.
Gunfire was heard after the explosion, according to news accounts. The consulate is on a major thoroughfare with a steady flow of traffic.
Photos from the scene showed a thick plume of black smoke rising above the Ankawa neighborhood.
Islamic State took responsibility in a Twitter message, said SITE, a private intelligence website that monitors militant Web traffic. The militants said the consulate was the target.
Irbil has been spared much of the violence that has convulsed Iraq since June, when Islamic State militants swept through a vast swath of northern and central Iraq. The militants advanced to within 25 miles or so of the Kurdish capital before being pushed back by U.S. airstrikes and Kurdish peshmerga ground forces.
In ordering the airstrikes against Islamic State targets last year, President Obama noted the large presence of U.S. citizens in Irbil. Washington is closely allied with the semi-autonomous Kurdish government.
Special correspondent Nabih Bulos in Amman, Jordan, contributed to this report.