Casualties from the blast were being taken to the hospital, police said.
The blast occurred at 3:00pm (10:30 GMT) on Saturday near a compound where Afghanistan's security agreement with the United States was to be debated by a Loya Jirga.
"The suicide attacker has detonated his explosive-packed car in an area packed with civilians," police chief Mohammad Zaher told AFP. "There have been casualties."
Afghan officials said that the bomber was targeting a vehicle carrying Afghan National Army (ANA) personnel.
About 3,000 elders are to meet next week for the Loya Jirga, a traditional meeting of elders, to debate the agreement, which would allow US troops to remain in Afghanistan after the final withdrawal of international combat troops at the end of 2014.
The explosion came just hours after President Hamid Karzai announced the final draft of the agreement had been completed, after lengthy negotiations between Afghan and US officials.
Karzai also said, however, that disagreements remain between the two countries over specific clauses of the agreement.