The joint operations force said the aircraft went down in eastern parts of the city, where government forces, the Kurdish Peshmerga and international allies are battling to dislodge jihadis.
It had been providing air support to Federal Police forces battling militants on the ground, according to military officials.
The helicopter was hit by a rocket launched from western Mosul, where Isis militants are holding out in areas housing an estimated 400,000 people, Kurdish broadcaster Rudaw reported.
Footage from an Associated Press cameraman showed it falling out of the sky in a large ball of fire with a long trail of thick black smoke on Thursday afternoon.
It is the first aircraft downed by Islamic State over Mosul since the start of the US-led coalition backed offensive in October.
Extremists have fought the advance using mines, booby traps, snipers, ambushes and suicide bombings in densely populated districts, where militants have been using civilians as human shields.
Progress has slowed in the narrow lanes of Mosul’s Old City, which Isis had prepared by making tunnels between buildings, screening streets from view with sheets and planting explosives.
“Daesh fighters are resisting on a professional level because they have no escape routes left,” said federal police officer Hussein Qassem.
“They are resisting until they are killed. God willing we will not leave any Islamic State fighters. We will fight till the end.”
Isis has previously claimed to shoot down helicopters in Syria.
The group has since lost almost all of its major strongholds, with Mosul the last city remaining under its control in Iraq.
More than 302,000 people have fled Mosul since the start of the offensive, with the International Organization for Migration saying 30,000 people were displaced last week alone.
Isis’ leader Abu Bakr al-Baghdadi announced the formation of the group’s self-declared “caliphate” from Mosul’s historic al-Nuri mosque in 2014.
The so-called Islamic State’s de-facto capital is the city of Raqqa in neighbouring Syria, which has been isolated by Kurdish-led forces in preparation for an offensive.
Additional reporting by Reuters
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