The first explosion occurred on the road used by families to flee from al-Shirqat, a village between the provinces of Saladin and Nineveh, Efe news reported.
Seven members of a family, including four children, were killed in the blast as they fled towards Iraqi troops that were deployed to the West.
A second explosion killed four people and injured two, who were all escaping from al-Hawiyah, 55 kilometers (34 miles) south of Kirkuk.
The victims were attempting to reach Kurdish Peshmerga forces, allied to the Iraqi Army.
Iraqi security forces started to besiege al-Shirqat and al-Hawiyah a few weeks ago, having cut off supply lines between these cities and Mosul, the IS' bastion in Iraq, Efe news added.
The two towns suffered a critical humanitarian crisis due to the lack of food and medical supplies, which pushed many civilians to leave.
However, dozens were killed in their attempts to flee by explosives planted by the IS.
Iraqi forces, including Sunni militias and the Kurdish Peshmerga, have slowly gained ground in the region.
Mosul was captured by the IS in June 2014, when the group declared a caliphate in the conquered Iraqi and Syrian territories.
