The blast took place at the Kaaj education centre in the Dasht-e-Barchi area in the west of the city.
Nearly every Friday, explosions have targeted places of worship and other institutions in Afghanistan, carried out by the radical Islamic State group despite the Taliban takeover of the country a year ago, The Washington Post reported.
Police spokesman Khalid Zadran said 19 were killed and 27 wounded, but the toll is likely to climb.
The United Nations Children's Fund (Unicef) yesterday condemned the blast in the western Kabul area of Afghanistan.
Unicef said this "heinous act" claimed the lives of dozens of adolescent girls and boys and severely injured many more.
"Unicef is appalled by the horrific attack, early this morning, inside the Kaaj Educational Center in the Dasht-e-Barchi district of West #Kabul, #Afghanistan," Unicef said in a tweet.
"Such places must be havens of peace where children can learn, be with friends, and feel safe as they build skills for their futures. Children and adolescents are not, and must never be, the target of violence," Unicef said in another tweet.
UNICEF is appalled by the horrific attack, early this morning, inside the Kaaj Educational Center in the Dasht-e-Barchi district of West #Kabul, #Afghanistan.
This heinous act claimed the lives of dozens of adolescent girls and boys and severely injured many more. pic.twitter.com/xWj7L7p95o
According to authorities, the target was an education centre in the Dasht-i-Barchi neighbourhood, which is predominantly populated by ethnic Hazaras, a mostly Shiite Muslim group, citing a Washington Post report.
Eyewitnesses told the BBC that most of the victims were girls. A student who was wounded told AFP that there were around 600 people in the room when the attack happened, international media outlets reported on yesterday morning.
Fuerte explosión en centro de estudios en Kabul.
— Janosik García (@Janosikgarciaz) September 30, 2022
Imágenes sensibles.
Información en desarrollo.pic.twitter.com/a8RG5jzIjz