The attack on a Shia mosque last week was likely aimed at sowing sectarian discord in a nation that is a key mediator.
In the first six months of the year, the group has claimed 153 attacks in Syria and Iraq.
The woman was charged with collaborating with ISIL and keeping kidnapped Yazidi women in her home in Mosul.
Iraqi authorities requested UNESCO halt all reconstruction operations at al-Nuri Mosque and evacuate the entire complex.