Another member of the Romanian military service was also killed, the NATO-led coalition said in a statement.
The attack had not penetrated into the security area, the official said.
Further details are not available immediately. The identity of the American will be announced 24 hours after the next of kin has been informed.
The US will withdraw troops from five bases throughout Afghanistan within 135 days, as long as the Taliban fulfill the conditions set out in the agreement.
The withdrawal of US troops could mark the beginning of the end of the longest American war, a nearly 18-year conflict triggered by the terrorist attacks of September 11, 2001, which cost billions in taxpayer money and cost more than 2,300 American lives.