It says the soldier was killed while fighting IS in Nangarhar province in eastern Afghanistan.
Nangarhar province borders Pakistan and has a reputation for being a centre of IS militancy.
US forces have launched several air strikes on jihadist bases in the area.
IS announced the establishment of its Khorasan branch - an old name for Afghanistan and surrounding areas - in January 2015. It was the first time that IS had officially spread outside the Arab world.
Within a few weeks, the group appeared in at least five Afghan provinces. including Helmand, Zabul, Farah, Logar and Nangarhar, trying to establish pockets of territory from which to expand.
IS in Afghanistan: How successful has the group been?
It was the first major militant group to directly challenge the Afghan Taliban's dominance over the local insurgency.
Yet despite efforts to energise battle-weary militants, IS struggled to build a wide political base and the indigenous support it expected in Afghanistan. Instead, it made enemies of almost everyone, including the Afghan Taliban.