The car bomber targeted a police and intelligence compound in Nangarhar province's Pachir Wagam district, said provincial spokesman Ahmad Zia Abdulzai.
In an emailed statement, the Taliban claimed responsibility for the attack, which also wounded three members of the Afghan security forces.
Insurgents in Afghanistan have intensified attacks recently in a campaign to regain territory as foreign forces prepare to leave the country at the end of 2014.
Also in Nangarhar province today, a would-be suicide bomber was shot by officers as he tried to attack the home of a member of Afghanistan's parliament in the city of Jalalabad, police said.
No one claimed responsibility for the botched attack, but the Taliban have in the past targeted prominent Afghans who are opposed to the insurgency.