The bombing, similar to attacks carried out by insurgents against Afghan and Nato forces, killed a local police commander who was the apparent target of the blast, said provincial governor Mehrabuddin Safi.
The explosion in Tagab, a troubled district in the province of Kapisa, was set off by remote control and also killed the police commander's son, two of his guards and two civilians, the interior ministry said in a statement.
Many of the 3,500 French troops operating in Afghanistan as part of Nato's International Security Assistance Force (ISAF) are deployed in Kapisa.
Seventeen civilians were wounded in the blast in the town's main bazaar, the governor and interior ministry said.
Homayoun Rashidi, a local police spokesman, said the bombing targeted a group commander in the US-funded semi-militia force known as the Afghan Local Police, which is tasked to fight insurgents in remote parts of the country.
Kapisa sees regular Taliban violence, mostly roadside bombings, suicide attacks and militant ambushes.
A security source said no French soldier was involved, but some of the wounded civilians were taken to the French military camp for treatment.
Four French troops and two of their Afghan interpreters were killed in a suicide bomb attack on June 9 which was claimed by the Taliban.