Abdullah al-Badrani, also known as Abu Ayoub al-Atar, reportedly died in an air strike by the US-led coalition on Thursday.
Al-Badrani issued many of the group's dictates, leading to the torture, death and sexual abuse of civilians.
Iraqi security forces are trying to retake al-Nuri mosque in the old city.
The Islamic State group has made its name feared and reviled through the very public atrocities and human rights abuses it has committed against whole communities.
Abu Ayoub al-Atar was infamous in Mosul and beyond for the religious decisions - or fatwas - he issued that permitted some of these acts.
He is believed to have given the justification for the enslavement and sexual abuse of women from the Yazidi minority in northern Iraq.
More recently, he has given the authority for IS to continue to attack civilians in the eastern side of Mosul, which Iraqi forces have recaptured.
He called the civilians apostates who deserve to be killed.
The Iraqi government has issued instructions to civilians on how to stay safe as forces continue their assault on the IS-held western side of the city.
Al-Nuri mosque is a significant target as it is where IS leader Abu Bakr al-Baghdadi first appeared after the declaration of caliphate across parts of Iraq and Syria in 2014.
One of the most senior religious leaders in the Islamic State (IS) group has been killed in west Mosul, according to Iraqi forces.