In an announcement on Tuesday, the office said the crescent of the holy month is most probably going to be sighted on Wednesday evening, al-Sumaria news website reported.
It added that, therefore, Thursday will be the first day of Ramadan in Iraq and elsewhere in the Middle East.
Muslims in a number of other countries, including Iran, Oman, Yemen, Saudi Arabia and Indonesia will also begin fasting on Thursday.
Muslims around the world are set to mark the month, during which believers abstain from eating, drinking and smoking from dawn until after sunset.
Fasting is intended to bring Muslims closer to Allah and remind them of those less fortunate.
The Islamic world follows a lunar calendar, and the traditional moon-sighting methodology can lead to different countries declaring the start of Ramadan a day or two apart.