The dead include three Nepalese and one Peruvian. Their names were not released. Seven others were injured in the attack.
The Taliban bomber, riding an explosive-laden motorcycle, was dressed in the same uniform as the security contractors, which Kabul police spokesman Hashmatullah Stanikzai said enabled him to breach a checkpoint manned by Afghan police.
Driving into the compound, he detonated himself outside the building used by DynCorp trainers.
A NATO official, speaking on the condition of anonymity, told the New York Times that it was possible the bombing was an inside job, noting that the Afghan bomber was wearing a foreign security contractor's uniform, which would "strike me as more suspicious, not less, right?"
Tuesday's attack comes less than a week after the Taliban launched a brazen attack against Kabul International Airport.