The helicopter - the second lost by Iraq in two days - went down near Amriyat al-Fallujah, though officials differed on the exact location.
An Iraqi army aviation captain said that the Bell helicopter was shot down with a Dushka heavy machine gun, killing one crew member and wounding a second, who was rescued by another helicopter.
Lieutenant Colonel Arif al-Janabi, the police chief for Amriyat al-Fallujah, said that IS shot the helicopter down, putting the death toll at two.
IS issued an online statement claiming that it shot a helicopter down and damaged another in the Amriyat al-Fallujah area yesterday.
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Iraq has lost multiple helicopters to accidents and ground fire in recent years, while others have been damaged.
An Iraqi Mi-17 helicopter crashed south of Baghdad due to a "technical problem" yesterday, killing nine people.
In October 2014, militants shot down a Bell 407 north of Baghdad, killing two crew, five days after an Mi-35 was shot down in the same area, while jihadists destroyed another helicopter on the ground earlier in the year.
Lieutenant General Hassan Karim Khudayr was killed when a military helicopter crashed north of Baghdad before IS launched a sweeping offensive in June 2014. Iraq also lost an Mi-17 to a sandstorm in July 2010, a crash that killed five.