The terrorist group, which has declared an Islamic caliphate in parts of northern Iraq, says reading the Quran before and after prayers is a Bid'ah (illegitimate innovation), al-Sumaria news network reported.
The militants also prevent prayers leaders from entering mosques in city of Fallujah in northern Iraq and do not allow people to hold ceremonies to mourn the death of their loved ones.
The crisis in Iraq escalated after the ISIL militants took control of Mosul in a lightning attack on June 10, which was followed by the fall of Tikrit, located 140 kilometers (87 miles) northwest of the Iraqi capital Baghdad and Fallujah. Tikrit was later taken back by the Iraqi army forces.
An estimated 1.2 million people have been displaced in Iraq so far this year, according to the United Nations.
The ISIL has vowed to continue its raid towards Baghdad.