The bombing was the second in the capital in as many days after 10 people were killed on Friday when a bomb ripped through a mosque as worshippers were performing rituals.
No group claimed Friday’s mosque bombing but IS took responsibility for the attack on the bus.
IS has claimed several bombings in recent weeks, particularly attacks targeting Sunni-majority Afghanistan’s minority Shiite and Sufi communities.
Taliban officials insist their forces have defeated IS, but analysts say the jihadist group remains a key security challenge.
Kabul police meanwhile vowed to “ensure security” during the Eid al-Fitr holiday that marks the end of Ramadan.