The Supreme Judicial Council said in a statement that the Central Criminal Court sentenced three Azerbaijanis and one Kergyz to death, while issuing a life sentence for two Russians and a French national.
Earlier news reports quoted AFP identifying the French nationa as 29-year-old Jamila Botoato.
In February, Iraq sentenced a French woman to seven months in jail for entering the country illegally. In the same month, 16 Turkish women were sentenced to death for providing logistical support to the militants.
Iraq is holding hundreds of foreign wives and children of Islamic State militants who were captured as Iraqi forces gradually seized back territories held by the extremist group since 2014. The government declared victory over IS last December.
Authorities say they are coordinating with other countries to extradite those held who are not convicted of terrorism.