The two-man crew was killed when their helicopter "crashed in a swampy area north of Taji", it said in a statement.
"The aircraft was conducting a combat air patrol. It is premature to determine the cause of the crash."
It was the third US chopper lost in 10 days in Iraq.
A journalist for Dubai-based Al-Arabiya television station, speaking from the scene, said the helicopter plunged to earth in a ball of flames after being hit by a rocket.
Al-Arabiya later showed video of that it claimed was made by a little-known Islamist group, Salahu Din al-Ayubi (Saladin) Brigades.
The video showed a rocket hitting a flying object and a plume of smoke.
The group claimed in an Internet statement it used rockets to shoot down the Apache.
Two other US pilots were killed on Friday when their reconnaissance helicopter was apparently shot down in the north of the country.
Eight US soldiers and four civilians perished a week earlier when their Black Hawk helicopter crashed near the restive town of Tal Afar in northwest Iraq.
Votes cancelled
Meanwhile the body in charge of last month's Iraqi elections has cancelled a small number of ballots, paving the way for final but uncertified results to be issued later this week.
Iraqi and US officials hope the creation of a unified government following elections on December 15 will help to undermine the Sunni-backed insurgency.
Initial indications showed Iraq's Shiite majority came out on top in the poll, but final results have been delayed by the electoral commission's probe, which was launched after Sunni-backed and secular parties complained of fraud.
The commission said on Monday that it had annulled the results of 227 ballot boxes out of a total of some 31,500 after finding evidence of fraud.
But "the number of votes annulled is not sufficient to change the overall result of the election," commission member Abdul Hussein al-Hindawi told a news briefing in Baghdad. He did not specify how many votes were cancelled.
The news came as a court official said the trial of deposed dictator Saddam Hussein would resume next week without its chief judge who handed in his notice earlier this month following criticism over how he ran the court.
An official at the Iraqi High Tribunal, which is trying Saddam and seven co-defendants, said judge Rizkar Mohammed Amin "will certainly not be present at the hearing on January 24" when the trial resumes.
The head of the tribunal, however, had yet to appoint his replacement. "It could be Saeed al-Hameesh," the only other judge on the panel of five to have been publicly identified to date, the official said.
Judge Amin handed in his notice more than six days ago.
Saddam and seven former aides are on trial for ordering the massacre of more than 140 Shiites from the town of Dujail following a 1982 assassination attempt on the former Iraqi leader.