The incident happened at around 7:20 am local time in Sar-e-Kotal area in Kabul's district 17, police said.
Sources said the bus carried employees of the Ministry of Communication and Information Technology.
The victims have been taken to a nearby hospital, eyewitness said.
No group has claimed responsibility for the blast.
This comes as five civilians, including four women – one of them pregnant – and a child, were killed in an explosion in downtown Kabul that targeted a bus carrying employees of two government ministries on Monday afternoon.
At least 13 others, all civilians, were wounded in the explosion, according to officials.
Figures collected by TOLOnews show that 144 people have been killed and 214 others have been wounded in different security incidents in the last 18 days.