Gunmen stormed Kabul University on Monday, killing students in their classrooms and firing on others as they fled.
It is the second attack on an educational institution in the city in just over a week.
The three attackers killed at least 19 people including students before Afghan security forces shot the gunmen dead, authorities said.
"They were shooting at every student they saw ... they even shot at the students who were running away," witness Fathullah Moradi told Reuters.
The Taliban said their fighters were not involved in the assault. No other group immediately claimed responsibility.
Nineteen people were killed and 22 wounded before the security services ended the assault, interior ministry spokesman Tariq Arian said.
"This is the second attack on educational institutions in Kabul ... Afghan children & youth need to feel safe going to school," NATO Senior Civilian Representative to Afghanistan, Stefano Pontecorvo said in a statement.
A suicide bomber killed 24 people including teenage students at an education centre in Kabul on October 24. IS claimed responsibility for that attack, without providing evidence.
Violence has plagued Afghanistan while government and Taliban negotiators have been trying to broker a peace deal and as the United States brings home its troops.


Fire in rebel-held east Congo kills 24 schoolchildren
Trump touts $5,000 payout if Republicans win as Vance waits in wings
Search expands after Philippine ferry fire kills five and leaves dozens missing
Trump says Iran war to end after US midterm elections
At least 20 killed in cargo vessel fire at China shipyard, state media reports
US military says it struck vessel in Caribbean, killing 3
At least 14 killed in explosion at weapons depot in Syria
US hits five Iranian oil tankers after attack on Navy ships
