Three vehicles and 15 shops were damaged or destroyed.
The district where the blast occurred is home to many of the minority Shia Hazara community.
The blast was close to the home of deputy government Chief Executive Mohammad Mohaqiq, a leader of the Hazara community.
There have been several recent attacks in the district, including one that killed senior Shia cleric Ramazan Hussainzada last month.
President Ashraf Ghani condemned the latest attack on "civilians and government staff", while the interior ministry denounced it as "a criminal act against humanity".
A Taliban spokesman claimed the bus had been under surveillance for months and was carrying "intelligence workers".
According to the United Nations, the country has seen at least 1,662 civilian deaths in the first half of the year with around 20% of those in the capital.
EPA
On 31 May, a huge bombing in central Kabul killed more than 150 people, the deadliest militant attack in the country since US-led forces ousted the Taliban from power in 2001.
Last month, at least 34 people were killed and 58 injured when a car bomb was detonated outside a bank in the southern province of Helmand.
US President Donald Trump is weighing up whether to increase the number of US troops who are aiding the Afghan military and police.
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