The attack in western Kabul also wounded four civilians and a foreigner, said Gen. Ali Shah Paktiawal. He said a NATO vehicle and seven civilian vehicles were damaged in the attack. The bomber also died.
Zabiullah Mujahid, who claims to speak for the Taliban, claimed the group's responsibility for the blast.
NATO's International Security Assistance Force said it was looking into the report of the attack, but had no immediate information.
Witnesses gave a higher casualty count than police, saying seven or eight people had died.
The blast came amid a wave of violence lashing Afghanistan, particularly the volatile south, including a homicide blast on Friday that targeted a NATO convoy at Tirin Kot in Uruzgan province, killing 10 people including five children and a Dutch soldier.
Kabul has been spared the worst of this year's bloodshed which has claimed 2,300 lives so far, mostly insurgents, according to an Associated Press count based on figures from U.S., NATO, U.N. and Afghan officials.
Saturday's blast destroyed the attacker's car, wrecked other civilian vehicles including a taxi and shattered windows of roadside homes and shops.
"We were busy with our work making window frames. I heard a very strong sound, and when I turned around I saw a big fire in the street," said Mohammed Noor, 22, who owns a nearby carpentry shop. He said the blast fired bits of metal shorn from the attacker's car into his shop front.
Noor said he helped four seriously wounded people into cars to ferry them to hospital. He said at least seven people were killed and 10 were wounded — a higher casualty toll than police offered.
The bomb apparently targeted a three-vehicle convoy of SUVs, damaging one although it was able to continue driving a quarter-mile down the road before coming to a halt with a punctured tire. U.S. armored jeeps arrived at the scene afterward suggesting the three SUVs may have been carrying American personnel.
Paktiawal gave no details on the nationality of the wounded foreigner.
Children from a school about 100 yards from the blast site looked on as investigators examined the wrecked vehicles.
This spring supporters of the Taliban regime ousted by U.S.-led forces in late 2001 have increased bombings and suicide attacks, but NATO and US forces claim to have the rebels on the back foot with a wave of offensive operations in the south and east.
Taliban spokesmen have warned Afghan civilians to stay away from military convoys, saying militants do not intend to kill them, but homicide bombings commonly kill or wound far more civilians than military targets — a fact NATO repeatedly points out.