There was no immediate claim of responsibility for the latest deadly attack in the Afghan capital that occurs days after a double bombing in a fighting club killed at least 26 people.
At least seven people were killed and 24 were injured in the blast, the interior ministry said in a statement. All the casualties were civilians.
The force of the explosion shattered the windows and shook nearby buildings.
Among the dead was the driver of a car that participated in the commemorations. He deviated from the highway and entered the front of a store when the explosion occurred, witnesses told AFP.
Two of his passengers were injured, they said.
Afghan security forces said earlier that they had shot dead a man who planned to fly near supporters of Ahmad Shah Massoud.
The Tajik commander led the resistance to the Soviet occupation in the 1980s and the Taliban regime of 1996-2001.
The attack occurred when convoys of armed men terrorized Kabul as they commemorated the 17th anniversary of Massoud's death.
Massoud was killed two days before the September 11 attacks in New York and Washington that precipitated the US-led invasion of Afghanistan.
Dozens of cars and trucks carrying men armed with heavy weapons and waving flags toured the city, blowing sirens. AFP journalists heard frequent bursts of gunfire.
At least 13 people were injured by bullets that fell and were taken to the hospital, health ministry spokesman Waheed Majroh told reporters.
Police arrested 110 people and confiscated 20 cars and 10 weapons, the interior ministry said, as part of a campaign against violent commemorations.
Elsewhere, almost 20 members of the Afghan security forces were killed in fighting during the night, which added to the hundreds of people killed in recent weeks.
Ten policemen were killed and eight wounded in an hour-long shootout with Taliban fighters in Wardak province near Kabul, spokesman for provincial governor Abdul Rahman Mangal told AFP.
"Air strikes were called and more than 50 Taliban fighters were killed" in the clashes in Daimirdad district, Mangal added.
On the other side of the country, Taliban fighters attacked a checkpoint in the Obe district of Herat province, killing nine members of the security forces, the spokesman for provincial governor Jailani Farhad told AFP.
Five others were wounded in the attack that ended when government-backed reinforcements were sent to the scene, Farhad said, adding that 15 insurgents were killed.
& # 39; Empire of the law & # 39;
The bloodshed comes amid a flurry of diplomatic efforts to convince the Taliban, the largest militant group in Afghanistan, to agree to negotiate an end to the war.
The smallest but most powerful group of the Islamic State (IS) is not part of the process, with the United States promising to annihilate its fighters in Afghanistan.
But Sunday's flagrant anarchy in the capital and the limited response of the security forces further undermined confidence in the authorities.
In a storm of angry social media messages, Afghans tired of the war expressed their frustration with the constant violence and inability of the government to protect civilians.
"Why do people have to endure this every year on September 9? Why does the #Afghan government allow it?" a user of social networks published on Twitter.
"Where is the rule of law?" tweeted another
A double bombing in a fighting club in a heavily Shiite neighborhood on Wednesday killed at least 26 people, including two journalists, and wounded 91.
The responsibility of the attack is claimed.
The extremist group considers the Shiite Muslims apostates and has intensified the attacks against the minority community in recent years.
The last major attack claimed by IS against the Shiites in Kabul was on August 15 when a suicide bomber blew himself up in an educational center, killing dozens of students.