At least 14 others were wounded in the blast. The Taliban said one of their suicide bombers carried out the attack.
The attack is being seen as a major security breach in one of the best protected places in Afghanistan.
The bomb reportedly exploded inside the base, which if confirmed, would be the first attack of its kind.
Attacks on Bagram have occurred in the past but insurgents have never made it past the compound's outer walls.
Bagram, just north of the capital Kabul, has been used as the main military base and airfield by the US-led forces and Nato over the past 14 years.
A local government spokesman was quoted as saying the attacker entered the base early in the morning on foot hidden among a group of workers reporting for duty.