According to Petra news agency, the Takfiri group has named the mosque after its leader Abu Bakr al-Baghdadi.
The militants are said to have forced people to pay for the construction of the mosque.
ISIL launched an offensive in Iraq in June last year and took control of Mosul, the country’s second-largest city, before sweeping through parts of the country’s heartland.
They have been committing heinous crimes in the areas they have taken, including the mass execution of civilians.
The group’s leader al-Baghdadi was seriously injured in March and it was reported that while his wounds were initially life threatening, he had slowly recovered from his injuries.