Three other servicemembers were wounded and have been evacuated for treatment, according to a statement by Resolute Support, the NATO-led mission in Afghanistan.
The attack comes as Washington is in the process of negotiating a military exit from the Central Asian country with the Taliban, the primary military and political antagonist to the Washington-backed government in Kabul. Two rounds of negotiations have taken place so far this year and a third is expected this month.
Several news outlets have reported that the Taliban has claimed responsibility for the blast.
This is far from the first exchange of violence during the negotiations. Last month, US and Taliban forces were locked in an intense battle near the northern city of Kunduz, Sputnik reported. US forces also accidentally attacked an Afghan army base in south-central Uruzgan province that fired on them in March, having assumed the US forces to be Taliban and vice-versa. The battle ended with an airstrike that destroyed the base.
Bagram Air Force Base is the largest US base in Afghanistan, located in the geographic east of the country.