U.S. Army Maj. Martyn Crighton said the soldier was among the 1,560 troops from the former Soviet republic of Georgia serving in the country.
A statement from Georgia's Defense Ministry on Thursday said an intense "search and rescue" operation was being mounted in Helmand and Nimroz provinces, describing the soldier as a military officer who went missing on Wednesday.
The last known coalition soldier to go missing was U.S. Army Sgt. Bowe Bergdahl, 26, who was taken prisoner on June 30, 2009 in Paktika province in southeastern Afghanistan.
Bergdahl, who turned 26 in captivity on March 28, was the subject of a proposed prisoner swap in which the Obama administration was considering the transfer of five Taliban prisoners long held at the U.S. military prison at Guantanamo Bay, Cuba, to Qatar.
That plan collapsed, but a new proposal would transfer some Taliban fighters or their affiliates out of full U.S. control. The prisoners would go to a detention facility adjacent to Bagram air field, the largest U.S. military base in Afghanistan, officials of both governments have said.
Eighteen Georgian soldiers have been killed since the country joined the international military
There are currently more than 102,000 coalition troops in the country, including 66,000 from the United States. Only a residual force is slated to remain past 2013.