The attack was the first major blast in the Afghan capital since Taliban militants launched a suicide attack on January 17 against a popular restaurant killing 21 people, including 13 foreigners.
"The bomber was on foot when he detonated himself next to a bus carrying Ministry of Defence staff to work," interior ministry spokesman Seddiq Seddiqi told AFP.
"Initial reports from the police say that three people in the bus were killed and one female bystander."
A Taliban spokesman using a recognised Twitter account claimed responsibility for the blast.
NATO combat forces are withdrawing from Afghanistan this year after more than a decade of fighting the Taliban, but negotiations have stalled over a deal to allow some US and NATO troops to stay after 2014.
Afghanistan's fledgling security forces face a difficult year in 2014 as insurgents attempt to disrupt elections on April 5 that will choose a successor to President Hamid Karzai, and as NATO's combat mission winds down.
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