The blast, caused by a remote-controlled bomb, targeted an Afghan army bus at around 06:45 am (0215 GMT) in the western part of Kabul, the Ministry of Defence said.
"In a remote-controlled bomb attack against an army bus at 6:45 am in Aqa Ali Shams in Kabul, four army personnel were killed and 12 wounded, including six civilians," the ministry said in a statement.
The Taliban, who have this year stepped up their attacks against the Afghan security forces, claimed responsibility via their official Twitter account.
A residual force of 9,800 US troops will remain, however, under a US-Afghan security agreement signed last month.
Afghan casualties have rocketed over the past two years as NATO has handed over most combat duties to the nation's police and army.
The US military estimated this month that 7,000-9,000 Afghan police or troops had been killed or wounded so far this year.