The spokesman, Bashir Ahmadi, said that five other passengers were wounded in the blast, and that all passengers were civilian passengers. Their bus collided with the explosive device.
The bombing is the third since the ceasefire ended briefly, which the Taliban announced during Eid al-Fitr last month.
The Taliban have not claimed responsibility for any of these attacks, but have said they have carried out a single attack targeting Afghan forces since Eid al-Fitr.
A bomb exploded inside a mosque in Kabul on Tuesday evening, killing two people, including the imam of the mosque, and wounding eight others.
ISIS mercenaries on Tuesday claimed responsibility for a weekend blast that hit a bus of a local television station in Kabul, killing at least seven civilians, including a woman and several children.
Of note, Washington and the Taliban signed a peace agreement in Doha to start withdrawing American soldiers from Afghanistan after 18 years of war, on February 29.