Around 2,500 tribal elders and civil leaders are expected to take part in an assembly known as a "loya jirga" next Thursday, to decide whether to accept the draft Bilateral Security Agreement between Afghanistan and the US.
"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," he added.
Nasrullah, a witness, said: "I heard a big bang near the jirga site, later saw ambulances carrying people in blood. I saw at least three wounded in army uniforms."
"The attacker driving a vehicle had been identified and was being pursued by security forces. He detonated himself after police opened fire on his vehicle," a statement issued by interior ministry said.
Earlier in the day, President Hamid Karzai called on the Taliban and their allies to join the assembly.
"We invite them, please come to this national jirga of Afghanistan, raise your voice, raise your objection... And share your views," he told a news conference in Kabul.
These include a US demand to retain legal jurisdiction over its troops in Afghanistan, which would give them immunity from Afghan law. The request emerged as the main sticking point after Kerry's visit.
The Taliban, whose government was toppled by a US-led invasion in 2001, has rejected the jirga and warned members that they would be punished as "traitors" if they endorsed the deal.
If the agreement is passed by both loya jirga and parliament, between 5,000 and 10,000 US troops would stay in Afghanistan to help fight Al-Qaeda remnants and train the national army.
Washington had been pushing for the agreement to be signed by the end of October to allow the US-led NATO coalition to plan the withdrawal of its 75,000 combat troops by December 2014.