"People in the area are angry and have beaten a number of ambulance workers," he told reporters.
The blast comes as the US military continues to pull out its last remaining 2,500 troops from the country, despite faltering peace efforts between the Taliban and Afghan government to end a decades-long war in Afghanistan.
Officials have regularly blamed the Taliban for attacks in Kabul, which the insurgents have steadfastly denied.
The Taliban have largely refrained from launching major attacks in Kabul since February last year, when they signed a deal with the United States that paved the way for peace talks and withdrawal of the remaining US troops.
But the group has clashed in near daily battles in the rugged countryside with Afghan forces even as the US military continues its withdrawal.
The Dasht-e-Barchi neighbourhood has been a regular target of attacks from Sunni Islamist militants. In May last year a group of gunmen attacked a hospital in the area in a brazen daylight raid that left 25 people killed, including 16 mothers of new-born babies.
The hospital was supported by Doctors Without Borders, the international medical charity, which later pulled out of the project. No group claimed that attack, but Afghan president Ashraf Ghani blamed the Taliban and the Islamic State group.
On 24 October, a suicide bomber blew himself up at a tuition centre in the same district, killing 18 people including students in an attack that also went unclaimed.