Officials say another six were wounded in the attack which occurred as cadets were leaving the college, one of Afghanistan's main officer training academies.
A suicide bomber blew himself up at the entrance to a military training centre in the Afghan capital on Thursday, killing at least six people and wounding six, police and security officials said.
One official, who spoke on condition of anonymity, said the attacker detonated his explosives after being prevented from entering the Marshal Fahim National Defense University, to the west of Kabul.
The explosion occurred as cadets were leaving the college, which is one of Afghanistan's main officer training academies.
The attack came as Taliban representatives met senior Afghan politicians in Moscow as part of efforts to reach a settlement to end the 18-year-long conflict.
Daesh claimed responsibility for the attack.
The delegation led by chief Taliban negotiator Mullah Baradar Akhund, met politicians, including senior regional leaders and candidates challenging President Ashraf Ghani in this year's presidential election, amid gathering diplomatic efforts to end the war.
"We are satisfied, that was successful negotiations, and we hope to continue this tempo in the future," Mohammad Sohail Shaheen, the chief spokesman for the Taliban delegation, told reporters after the meeting.
The meeting between senior Taliban officials and a diverse group of politicians was the latest step in efforts to reach a peace settlement.
Shaheen said a ceasefire proposal had been discussed but he gave no details. He also repeated the Taliban demand that international forces must leave Afghanistan for any peace deal.
"End of any war is peace but that doesn't mean surrendering to the Taliban Islamic Emirates."
The Taliban have been talking for months with US diplomats to agree on the withdrawal of more than 20,000 international troops from Afghanistan in return for guarantees the country would not be used as a base for militant attacks.
But they have so far refused to deal directly with Ghani's government, which they consider an illegitimate foreign-appointed regime.
On the other side, there is widespread suspicion among many on the government side and among civil society groups that any deal with the Taliban could see a rollback of advances in areas like human rights and the status of women made since the Taliban were overthrown in 2001.
Fawzia Koofi, a prominent women's rights activist and former member of parliament who attended the meeting in Moscow, tweeted: "End of any war is peace but that doesn't mean surrendering to the Taliban Islamic Emirates."