The US military said in a statement on Wednesday that the attack happened on Tuesday near the eastern city of Ghazni, where an American unit was conducting operations to "disrupt enemy activity in the region."
The attack comes amid an upsurge in attacks by Taliban-led fighters in the south and east of the country ahead of September legislative elections.
On Monday, one US service member and at least 16 suspected Taliban fighters were killed in clashes in the volatile southern province of Zabul.
Last Thursday, two American troops drowned when their vehicle slid into a river near Jalalabad city, while a third was killed by a roadside bomb in Paktika province near the Pakistan border.
Officials have warned that the recent violence is likely to intensify ahead of the elections set for 18 September, considered a critical step towards stability in Afghanistan after years of war and civil strife.
More than 17,000 US troops are in Afghanistan, and more than 170 have died in and around the country since Operation Enduring Freedom began in late 2001 to oust the Taliban after the attacks on the United States on 11 September that year.