The Sunday bombings began with the detonation of a magnetic bomb attached under a van carrying officials headed to the Kabul Education University, interior ministry spokesman Nasrat Rahimi said.
Shortly afterwards, two more bombs that had been planted by the side of the road went off.
“In total, one Afghan civilian was martyred and 17 others, including a local journalist and five Afghan forces, have been slightly wounded,” Rahimi said.
The wounded journalist was apparently live-streaming the aftermath of the first explosion when the second bomb went off.
There was no immediate claim of responsibility, but both the Taliban and Daesh militants have carried out blasts in the past week.
On Friday, a Taliban car bomber killed at least four Afghan civilians and wounded four US troops in an attack on a US convoy in Kabul
A day earlier, at least six people were killed and 16 more wounded in a explosion outside a military academy in the capital, claimed by Daesh.
Eight Afghan police officers were killed on Saturday and seven others wounded in an attack in the eastern Ghazni city, provincial police spokesman Ahmad Khan Seera told AFP.
Violence across Afghanistan continues unabated despite the presence of foreign troops, led by the US.
The Taliban and the US are set to begin a new round of peace talks in Doha, Qatar this month.
On Saturday, the leader of the Taliban vowed to continue battling US forces until its objectives are fulfilled, saying the group aimed for “an end to the occupation and establishment of an Islamic system”.
He also gave little sign that the militants would repeat last year’s truce over the three-day Eid al-Fitr holiday, which led to unprecedented scenes of Taliban members and government soldiers mingling and even embracing in the streets of Kabul.