According to the military, the clash took place on Sunday, when a group of 15 to 20 militants attacked a US patrol in Helmand province's Gereshk district.
An interpreter, employed by the American forces, was also wounded in the attack.
The wounded soldier and the interpreter, as also the two wounded insurgents, were transported to Kandahar airfield for treatment.
The other rebels fled the area after the attack, and US ground troops and aircraft were searching for them.
The name of the slain soldier was withheld pending notification to his family.
The death brings to 172 the number of US troops killed in and around Afghanistan since 2001, according to the US Department of Defence website.