The explosion struck around dawn in Kabul's east, on the road to the city of Jalalabad, Afghan authorities said.
"A suicide bomber blew up his vehicle loaded with explosives in Qabil Bai," deputy interior minister General Mohammad Ayub Salangi said in a tweet, adding that "one person was killed and three injured in this attack".
A spokesman for NATO's International Security Assistance Force said there were "no ISAF casualties" in the attack.
No group has yet claimed responsibility for the bombing, but it had all the hallmarks of those carried out by the Taliban.
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Kabul was also rocked two weeks ago by a series of suicide attacks staged during the inauguration of new president Ashraf Ghani. More than a dozen people were killed in several attacks on Afghan security forces.
About 40,000 NATO troops are serving in Afghanistan, but their combat mission is scheduled to finish at the end of this year, and the Taliban's recent offensives have severely tested Afghan soldiers and police.