Jassem Mohammed al-Jaff announced that field teams received "26,000 displaced people from (west) Mosul during the past 10 days," a statement from the ministry said, AFP reported.
But the number who have fled is only a small fraction of the 750,000 people who are believed to have stayed on in west Mosul under Daesh rule.
The drive to retake the west of Mosul began on Feb. 19, after Iraqi troops retook the city's eastern side the previous month.
Daesh overran large areas north and west of Baghdad in 2014, but Iraqi forces have since regained most of the territory they lost.
The operation to retake Mosul -- the last Daesh-held city in the country -- was launched on Oct. 17.