Officials gave no further details in the announcement on December 23, and the name of the service member was withheld pending notification of family members.
AFP reported that the Taliban militant group had claimed responsibility for the attack on the U.S. service member.
In a WhatsApp message to the news agency, Taliban spokesman Zabihullah Mujahid said insurgents “blew up an American vehicle in Char Dara district of Kunduz” late on December 22.
At least 20 foreign service members have been killed this year in Afghanistan, and more than 2,400 U.S. forces have died in the nearly 18-year conflict.
Some 20,000 foreign troops — 12,000 to 14,000 from the United States — are in Afghanistan as part of a U.S.-led NATO mission to train, assist, and advise local troops.
U.S. forces also carry out counterterrorism operations against Islamist militant groups, including Al-Qaeda and the Taliban.
U.S. President Donald Trump is seeking to end the conflict and pull U.S. troops out of the country to fulfill a campaign promise he made in 2016.
U.S. special peace envoy Zalmay Khalilzad has met with Taliban leaders in Qatar and, at times, has appeared close to reaching a cease-fire deal with the extremist group.
However, Trump in September canceled a secret meeting in the United States that was to include Taliban leaders after the militant group carried out a car bombing in Kabul that killed 12 people, including a U.S. soldier.
Negotiators from both sides have since resumed talking, but the Taliban has to date rejected negotiations with the Afghan government, seeing it as a puppet of foreign powers.