The son was killed and at least 14 people, including his father, were wounded in the attack, according to Attaullah Khogyani, a spokesman for the provincial governor.
There was no immediate claim of responsibility.
Taliban spokesman Zabihullah Mujahid on his Twitter page denied responsibility for the attack. There have been several bomb blasts in Afghanistan over recent weeks at a time when efforts are underway to restart a peace process with the Taliban. Islamic State in the same city last week claimed their first attack on a major urban centre in Afghanistan with an assault on the Pakistani consulate that killed seven people.