Provincial spokesman Ahmad Zia Abdulzai says the incident took place early Tuesday on the outskirts of Jalalabad, Nangarhar's capital.
He says the target of the bomb is unknown.
No one has claimed responsibility for the attack, but most such bombings are carried out by the Taliban.
NATO also says one of its service members has been killed in eastern Afghanistan on Tuesday from a "direct fire" attack.
It provided no other details or the nationality of the service member.
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