In a statement, the military said Specialist Charley Hooser of the 1st Cavalry Division was sentenced to three years in jail after being convicted of one count of involuntary manslaughter and one count of making a false statement.
"The convictions stem from an incident on November 24, when Hooser killed an interpreter, shooting her in the head," the military said late on Saturday.
"Later that day, he made an official statement with the intent to deceive, denying involvement in the death of the civilian interpreter."
Another soldier from the 1st Cavalry Division, Specialist Rami Dajani, was sentenced to 18 months in jail for his role in the incident, the military said.
It said Dajani had supplied the gun that killed the interpreter and had later "made an official statement with the intent to deceive, denying involvement in the death of a civilian interpreter".
A killer joke
On the day of the incident, Dajani and 28-year-old Luma, whose full name was not disclosed, were in a room at an American base, joking about killing someone, the soldiers testified at the court martial hearing.
Dajani handed a handgun to Hooser, who thought it had been cleared and pulled the trigger as he held it to the young woman's head. The two GIs then lied to investigators, claiming that Luma had shot herself.
The woman had worked as a translator for The Washington Post daily before taking a job with the military.
Several US soldiers have been sentenced or are awaiting court martial in Iraq for their role in the killing of Iraqis. The scandal over abuse of prisoners at Abu Ghraib jail by US troops has also sparked widespread outrage.