The militants used a shoulder-fired missile to take down the Bell 407 north of Beiji, a military aviation official said.
The town, 130 miles north of the capital, is home to Iraq's largest oil refinery.
A Defence Ministry official confirmed the attack. This is the second Iraqi military helicopter shot down over Beiji by IS militants in a week. A Mi-35 was downed near Beiji on Friday, killing the pilot and co-pilot.