The attack came on the third day of the Muslim holy month in the war-torn country, where Taliban-led insurgents are fighting against the Western-backed government.
"This morning, a suicide bomber wearing a suicide vest detonated his explosives outside the city of Kabul," Kabul police chief, Mohammad Ayoub Salangi told AFP.
"The bomber was in a passenger Toyota sedan. Police stopped the vehicle and wanted to search everyone. The bomber ran away and blew himself up. As a result of the explosion, one passenger was killed and two others wounded," Salangi said.
There was no immediate claim of responsibility, but the Taliban last Friday vowed to increase their attacks during Ramadan. The insurgents have stepped up attacks on Afghan forces since they took responsibility for national security last month.
Some 100,000 US-led NATO troops in Afghanistan are preparing to withdraw from the country by the end of next year.
