The blast took place at the Kaaj education centre in the Dasht-e-Barchi area in the west of the city.
Police in Kabul say a suicide attack at a tuition centre in the Afghan capital has killed at least 19 people and injured many others.
The blast took place at the Kaaj education centre in the Dasht-e-Barchi area in the west of the city.
Students had been sitting a practice university exam, officials from the centre said.
Many of those living in the area are from the Hazara ethnic minority, which has been targeted in past attacks.
Footage on local TV and shared on social media appeared to show scenes from a nearby hospital, where rows of covered bodies were laid out on the floor. Other media reportedly from the site of the private college showed rubble and upturned tables in the damaged classrooms.
The Kaaj tuition centre is a private college which teaches both male and female students. Most girls’ schools in the country have been closed since the Taliban returned to power in August last year, but some private schools are open.
No group has yet said they are behind the blast.
But Hazaras, most of whom are Shia Muslims, have long faced persecution from both the militant Islamic State group (IS) and the Taliban, who both adhere to Sunni Islam.
On Friday the Taliban’s interior ministry spokesman said security teams were at the site and condemned the attack.
Abdul Nafy Takor said attacking civilian targets “proves the enemy’s inhuman cruelty and lack of moral standards.”
The Taliban says it is attempting to restore stability.
However attacks by IS have continued.
The Dasht-e-Barchi area has been the location of a series of attacks, some of which have targeted schools and hospitals.
Last year – before the Taliban returned to power – a bomb attack on a girls school in Dasht-e-Barchi killed at least 85 people, mainly students, and wounded hundreds more.