Three other people were left wounded in the explosion, which occurred during afternoon rush hour when employees of the ministry were likely to go home.
"Most of the people killed and wounded were civilians, but we don't know the exact target," interior ministry spokesman Najib Danish told AFP.
Islamic State group claimed the attack through its propaganda agency Amaq. It said the bomber had targeted a checkpoint outside the Afghan presidential palace.
But the group has been steadily losing territory in the face of heavy pressure from both US air strikes and a ground offensives led by Afghan forces.
Islamic State's strength has now depleted to 600-700 fighters from 3,000 in early 2016, NATO has said, adding that it killed the top 12 IS commanders in Afghanistan last year.
The jihadists also claimed a deadly assault on Afghanistan's largest military hospital last month, but survivors who spoke to AFP said the attackers chanted "Long live Taliban" in Pashto.
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