Taliban spokesman Zabiullah Mojahid claimed responsibility for the attack.
The explosion occurred around 12:45 p.m. local time after the vehicle passed through a security checkpoint, Interior Ministry spokesman Nasrat Rahimi told CNN.
Police identified the attacker at a second checkpoint but could not stop him before he detonated the explosives near the former Ministry of the Interior building, Rahimi said.
The wounded were taken to hospitals in the Afghan capital, said spokesman Wahid Majrooh of the Ministry of Public Health, who confirmed the casualties.
He also called on the international community to" take additional measures "against" state-sponsored terrorism. "
"Our priority and focus at this time is to help the needy and provide the best treatment for the injured," he wrote. "This is the time when we must all unite and hit our enemy hard. This is enough! "