The deaths were caused by insurgent "indirect fire," either mortars or rockets, said the official, who spoke on condition of anonymity.
The report of casualties came hours after the Taliban insurgency announced it would enter into peace talks with the Afghan government and the US, and after NATO formally handed responsibility for security to the Kabul government.
There were no further details of the attack at Bagram, a sprawling base about 30 miles (47 kilometres) north of Kabul that serves as a major hub for US aircraft.