The incident took place on Monday in Achin, Nangarhar province, the US military statement said on Tuesday.
The US military did not release additional details about the incident.
"We are deeply saddened by the loss of one of our own,” said Army General John Nicholson, commander of US forces in Afghanistan. "At this very difficult time our heartfelt sympathies go out to the families and friends of our fallen and wounded brothers."
According to the statement, two of the wounded service members are being treated at a medical facility and in stable condition.
In August, US President Donald Trump vowed to take a harsher stance in the so-called war on terror in the war-torn country.
He approved a Pentagon plan to deploy some 3,800 additional US forces to Afghanistan, where more than 11,000 are already serving.
The United States -- under Republican George W. Bush’s presidency -- and its allies invaded Afghanistan on October 7, 2001. The offensive removed the Taliban regime from power, but after 16 years, the foreign troops are still deployed to the country.
After becoming president in 2008, Barack Obama, a Democrat, vowed to end the war -- one of the longest conflicts in US history – but he failed to keep his promise.