The Black Hawk went down about four miles south of Fallujah, a stronghold of the anti-American insurgency, the 82nd Airborne Division said.
The military said the cause of the crash was not known, but a witness, Mohammed Ahmed al-Jamali, said he heard the distinctive whoosh of a rocket and saw the helicopter, which was clearly marked with red crosses signifying its medical mission, struck in the tail.
The 27-year-old farmer who lives close to the crash site said he rushed to the scene but found everyone dead.
The helicopter was a medical evacuation aircraft but it was unclear if it was carrying patients, a military official said, speaking on condition of anonymity.
Another witness, student Waleed Kurdi, 23, said he heard "a loud explosion and I saw the fire in the air" as the chopper exploded in two before it hit the ground.
Twice before, American helicopters have gone down near Fallujah, a city 35 miles west of Baghdad.
In other developments:
The 82nd Airborne Division said its paratroopers acted after receiving "two rounds of indirect fire" around 9 p.m. Tuesday.
The neighbors insisted the couple was innocent in an attack on the troops that led them to shell the house.
Civilian deaths in the counterinsurgency campaign have enraged many Iraqis at a time when the U.S.-led coalition is trying to win popular support.
The release of detainees was designed, in part, as a goodwill gesture to frustrated Iraqis.
On Wednesday, U.S. administrator L. Paul Bremer announced that authorities would release 506 of some 12,800 detainees in a goodwill gesture. He said the first 100 would be freed from Abu Ghraib on Thursday and the others over coming weeks from detention camps all over the country.
But a spokesman for the 800th Military Police brigade, the U.S. Army unit operating prisons in Iraq, said they had not received any order to release prisoners. "Until we get some information that says 'release these prisoners,' they are staying put," said a spokesman, Lt. Col. Roy Shere.
U.S. and coalition troops have rounded up thousands of people suspected of attacks or of funding the anti-American insurgency in Iraq.
From first light, people started arriving at the prison, some driving for hours in hopes that relatives arrested in raids and not seen for months would be among those released.
"I don't trust the Americans. They are making more enemies for themselves now by arresting innocent people," said Jassin Rasheed. He said his brother, Omar, was detained two months ago after he had a fight with a fellow security guard at an oil installation.
"For revenge, they told the Americans that my brother is a terrorist," Rasheed said.
There were many other claims of unjust detentions: Bedouins arrested as they tended their sheep; a son taken away because he was near the scene of an attack on American troops; a name given to U.S. troops to avenge some dispute; a father arrested because he had a rifle in his car.
"Everyone in Iraq has a gun," said Karim Mohammed, 30, who was detained along with his brother but released 10 days ago. He said police came to their home and asked for his brother by name, then arrested the two when they found an AK-47 in their home.