The attack happened late yesterday in the Shiite holy city of Samarra, about 95 kilometres north of Baghdad. A senior Defense Ministry official told The Associated Press the Sunni militants used a shoulder-fired rocket launcher to shoot down the EC635 helicopter on the outskirts of the city.
An army official corroborated the information. Both spoke on condition of anonymity as they weren't authorised to speak to journalists.
The militants shot down at least two other Iraqi military helicopters near the city of Beiji in October. Some fear the militants may have captured ground-to-air missiles capable of shooting down airplanes when they overran Iraqi and Syrian army bases this summer.
European airlines including Virgin Atlantic, KLM and Air France, US carrier Delta Air Lines and Dubai-based Emirates changed their commercial flight plans over the summer to avoid Iraqi airspace.
The Islamic State group holds about a third of Iraq and neighbouring Syria in its self-styled caliphate.
The Britain-based Syrian Observatory for Human Rights said the four were beheaded yesterday in the province's east, without elaborating.
A jihadi website said the "Islamic police in the state of Homs" carried out a court sentence against the four in the presences of onlookers. Grisly photos posted on the website showed each of the four blindfolded men kneeling, their hands tied behind their backs, as a masked man in a black uniform hit their necks with a cleaver.