The Taliban told the BBC they were responsible for the attack, the broadcaster reported.
The report said at least one police office was killed while many of the other casualties appeared to be civilians.
The attacker crashed a vehicle filled with explosives into into an Afghan army vehicle, police said. The soldiers inside the official vehicle opened fire on the suicide bomber before the explosion.
The blast occurred very near Burhanuddin Rabbani university, near a camp where Afghan tribal leaders are scheduled to meet next week to discuss a bilateral security agreement with the United States, Khaama Press reported..
The agreement would establish the status of 10,000 U.S. troops scheduled to stay in Afghanistan after most Western forces withdraw by the end of 2014, the BBC said.
The agreement must be approved by the Afghan parliament and the Loya Jirga council.