The military said that three other service members were wounded when the bomb went off near the city of Ghazni. An American contractor was also wounded, it said. The military did not immediately identify any of the casualties.
Lt. Ubon Mendie, a military spokesman, said the wounded were evacuated and are receiving medical care.
The Taliban claimed the attack, saying a U.S. tank was completely destroyed.
It appeared to be the deadliest attack on American forces since June 2017, when an Afghan army soldier shot and killed three U.S. soldiers in an insider attack in the Achin district of the eastern Nangarhar province. The Taliban claimed that attack.
The Taliban carry out near-daily attacks on Afghan forces, and in August the insurgents overran parts of Ghazni, leading to days of intense fighting before they were driven out. Ghazni was the only one of Afghanistan's 34 provinces where parliamentary elections could not be held in October. Voting there has been postponed for a year.
The U.S. and NATO formally concluded their combat mission in Afghanistan in 2014, but still provide close support to Afghan forces and carry out counterterrorism operations. Some 15,000 American forces are currently serving in Afghanistan.
In a separate incident on Tuesday, the Taliban abducted 21 passengers from two vans that were traveling through the northern Sari Pul province, according to Habibullah Mujahidzada, a district police chief. It was not immediately clear what motivated the abduction, and there was no immediate comment from the Taliban.