Locals, who witnessed the incident, reported seeing a missile hit one of two helicopters circling the area before the crash.
"I saw a missile hit one of the helicopters and black smoke come from it before it went down," one man, who gave his name as Abu Mustafa, told Reuters.
The military has not said what caused the crash, though in the past insurgents have shot down U.S. and other aircraft with shoulder-fired missiles and other small arms.
The incident was one of several acts of violence around the country Monday.
One U.S. soldier died from a gunshot wound while investigating a burning vehicle in Baghdad, the military said, and two civilians died when a roadside bomb went off in Aadhamiya, a Sunni neighborhood in Baghdad. Three other civilians were killed when gunmen fired on a barbershop in Baghdad overnight, killing the barber, one customer and a 9-year-old boy, according to Reuters.
Insurgents also targeted Iraqi police officials Monday, killing Kirkuk police Capt. Farhan Faisal in an ambush as he drove to work and police Maj. Mohammed Shamekh, who died in an attack at a Baghdad market.
Three Iraqi oil workers also died in a roadside bomb in Safraa, 43 miles south of Kirkuk.
Meanwhile, the military announced that the United States would build one new prison and expand several others in Iraq to house "security detainees" captured as part of the ongoing insurgency.
The military is currently holding more than 10,000 detainees in facilities in Iraq. The new construction will enable the detention of an additional 6,000 prisoners, military spokesman Lt. Guy Rudisill said.
As part of the development, U.S. forces will build a new prison at a former military barracks in Sulaimaniya 205 miles north of Baghdad. Camp Cropper near the Baghdad airport will be expanded to house 2,000 new prisoners in addition to the 125 already there. Former Iraq dictator Saddam Hussein is also jailed at Camp Cropper.
The military will also expand the largest run U.S. prison, Camp Bucca in the south of the country, to hold 1,400 new prisoners, and Abu Ghraib prison, notorious for reports of detainee abuses, will make room for an additional 400 prisoners.
The expansion of U.S. prison facilities is the result of "successful military operations against the insurgency and terrorists by coalition forces and the Iraqi special forces," Rudisill said.
Also Monday, British Prime Minister Tony Blair said British, U.S. and Iraqi officials have been negotiating with groups in Iraq who support the insurgency to try to fold them into the political process.
"Throughout the entirety of this we have been engaged perfectly properly in trying to pull away some parts of the insurgency to lock them into the political process," Blair said at a new conference.
Blair said the coalition would have no contact with extremists like al-Qaida leader Abu Musab al-Zarqawi and that the British government would not compromise its stance on terrorism.