The soldier, who has not been named by the US military, was taken out of the country "based on a legal recommendation," Pentagon spokesman Navy Capt. John Kirby said in Washington, the Associated Press reported.
"We do not have appropriate detention facilities in Afghanistan," Kirby said, referring to a facility for a US service member "in this kind of case."
However, the trial may still be held in Afghanistan, Kirby said.
A senior U.S. official, meantime, told NBC News that the soldier was moved to a detention facility in Kuwait, where a military lawyer from Joint Base Lewis-McChord was scheduled to meet with him.
According to NBC, the soldier has already appeared before a pre-trial confinement hearing and was ordered held without charges. He must face a second pre-trial confinement hearing within seven days, to determine whether he should remain in custody, and so on — a process that NBC wrote could go on for months before official charges are filed.
NBC cited officials as saying the military was considering filing capital murder charges, which carry the death penalty.
According to Reuters, Afghan President Hamid Karzai's office was understood to have accepted that the soldier be tried in a US court, provided the process was transparent and open to media.
However, the decision to move the soldier — reportedly made by the US military commander in Afghanistan, Gen. John Allen — has angered Afghan lawmakers.
Abdul Khaliq Balakarzai, a lawmaker from southern Kandahar province where the killings occurred, told the AP that trying the soldier in Afghanistan would be the best way for the US to show locals they want to punish him.
Mohammad Naeem Lalai Hamidzai, another Kandahar lawmaker, warned Afghans could rise up in anger.
The Taliban has already threatened to behead US personnel in retaliation for the attack, and insurgents on Tuesday attacked Afghan officials investigating the shootings.