Afghanistan's parliament has called on the government to prosecute the soldier even though the US military has said it believes that the crash on May 29 was an accident caused by brake failure.
The accident, in which the soldier's truck smashed into a dozen parked vehicles and killed the Afghans, triggered the worst riot in years.
Ronald Neumann, the US ambassador, said on Monday that an agreement reached in 2003 between both nations means the soldier could not face legal action in Afghanistan.
"There is a status of forces agreement and US retains criminal jurisdiction for acts committed by military personnel in Afghanistan," he said.
Afghanistan has started its own investigation into the crash.
The US military, which is also holding an inquiry, has said that it will co-operate with the Afghans.
The US military is also investigating whether its troops fired into a crowd of stone-throwing Afghans after the accident.
Observers believe that the riot that followed the crash stemmed from resentment towards the US military over the aggressive driving tactics of its troops.
Nuemann: US retains jurisdiction
for acts committed by army staff
Convoys often pass through crowded areas at high speed and sometimes disregard road rules.
Neumann said the United States has reduced the speed at which its vehicles drive.
"We actually slowed down convoys a great deal, including mine, some months ago," he said.
But he said the matter was being reviewed.
'Death to America'
Lieutenant-General David Richards, the commander of a 9,000-strong Nato-led peacekeeping force in the country, has said that foreign troops must stop driving aggressively because they risk alienating the local population.
During the riots, protesters rampaged through the capital, screaming "Death to America!".
They were the fiercest since the fall of the Taliban in 2001 and left about 20 people dead.