The helicopter crashed on Wednesday in Salahuddin province north of Baghdad near the Baiji oil refinery, the largest such facility in the country, according to an Iraqi army officer.
The officer confirmed two army personnel died, but said the crash was still under investigation.
IS said on Twitter that it downed the aircraft and published pictures that it claimed were of the debris and the corpse of one of the pilots.
The IS Twitter feed also included a photo of one of their fighters preparing to fire off a shoulder-held rocket or missile that the group said struck the helicopter.
The Baiji refinery, which remains under Iraqi military control, has been surrounded since June when IS fighters swept across northern Iraq, seizing most Sunni sections of the country from the Shia-led government in Baghdad.
IS fighters seized large numbers of shoulder-held missiles across the border from Iraq in Syria, where it has been fighting the Syrian government and other rebel factions.
The IS also looted most of the Iraqi military's weapons supply - including tanks, humvees and ammunition - across northern Iraq as the Iraqi security forces fled this June in the face of the militant' surprise offensive.
The IS has declared a Caliphate based on medieval beliefs in territory they control in Iraq and Syria.
In other violence in Iraq, a car bomb exploded in Baghdad's Shia district of Sadr City late on Wednesday, killing 19 people and wounding 39 others, according to police and hospital officials.
The bomb exploded in front of a police station and coffee shops and restaurants, where people were celebrating the Muslim holiday Eid al-Adha, the official said.
Bombs regularly target Baghdad's largest neighborhood, home to the country's Shi'ite majority population and some of the larger Shi'ite paramilitary groups.