The explosion occurred as a civilian vehicle drove over an improvised explosive planted along the road.
In a statement, the Taliban claimed that the target of the blast was a vehicle belonging to Afghan security forces, but hospital officials identified all the victims as civilians. Eyewitnesses said a vehicle belonging to the Afghan intelligence agency had previously passed along the same road.
Roadside bombs are a favorite tactic of Taliban-led insurgents and are among the leading causes of civilian casualties in Afghanistan.
The attack killed a man in his mid-40s who succumbed to his injuries shortly after arriving at the Ghazi Amanullah Khan Hospital in Kabul, hospital officials said.
Two of the three injury victims were being treated at the same hospital.
Also Tuesday, officials in the southern province of Helmand said that two senior Afghan police officers were killed and three wounded in an insider shooting by another officer.
The attack on Monday evening killed the chief of police in the district of Nowzad and a unit commander, officials said.
Police officials said the attacker was shot and killed.
Nowzad was a focal point for U.S. Marines based in Helmand until last year, and since the summer the Taliban has made gains in the area, causing some villagers to flee their homes.
Insider shootings have declined in recent years after a spate of such shootings by Afghan service members killed dozens of U.S. and international troops. Though the attacks on foreign forces made headlines, insider shootings more commonly target Afghan soldiers and police, officials say.
The violence comes as President Ashraf Ghani on Monday announced his list of Cabinet nominations, including new ministers in charge of the army and police, after a long delay. Afghans and foreign officials welcomed the announcement, more than three months after Ghani was inaugurated.