The Russian-made An-12 plane with up to seven crew members - none of them American - was flying from al-Asad air base to Baghdad International Airport when it lost radio contact and crashed around 11:35 a.m., the military said.
The crash happened south of Fallujah, where insurgents once held sway. The military said mechanical failure or pilot error was the likely cause, but declined to elaborate. The military also secured the crash site.
"It looks like everybody was lost but I can't confirm that. The investigation will determine that," U.S. military spokesman Capt. Charles Calio said.
Iraqi police in Fallujah said no shooting was reported at the time of the crash.
In a statement, FedEx said it was aware that an aircraft operated by one of its contractors to carry FedEx Express cargo could not be located on radar and had been out of radio contact since 10:45 a.m.
"FedEx is closely monitoring the situation and is working with the contractor to investigate the situation," the statement said. "Our foremost priority is the safety and welfare of the pilot and crew."
The U.S. logistics company said the aircraft had originally come from Dubai in the United Arab Emirates.
Also Thursday, the main U.N. envoy in Iraq, Staffan de Mistura, in a statement condemned the killing of two Christian sisters in the northern Iraqi city of Mosul.
Iraqi police say the two women were killed Wednesday as they were waiting in front of their house for a ride to work. Their mother was wounded in the attack.
The U.S. military has confirmed the killings and says the Christian family's house was then destroyed by bombs planted inside.
The attack came after about 13,000 Christians fled Mosul last month in the face of threats and attacks from extremists.
De Mistura noted that the killings followed a report by the U.N. High Commissioner for Refugees that some recently displaced Christian families were starting to return as the security situation in Mosul showed signs of improvement.
He also called on Iraqi authorities at the national and local level to protect Christians and other minorities in Iraq and to ensure those behind the attacks "are swiftly brought to justice."
Tensions are running high in Mosul, where U.S. and Iraqi troops have been trying since last spring to rout insurgents from Iraq's third largest city.
On Wednesday, an Iraqi soldier opened fire on a group of U.S. soldiers at an Iraqi military base in Mosul, killing two of them and wounding six others before dying in a hail of bullets, U.S. and Iraqi officials said.
The attack remained under investigation.