Mirwais Sadiq was killed in the western city of Herat. The BBC said that according to one report, he died after a rocket propelled grenade hit his car. State television said the security commander for Herat, the city's director of narcotics control, and a bodyguard also died in the attack.
The BBC said the attack followed a failed bid to kill his father, the governor of Herat.
After Sadiq's death, fighting broke out between troops loyal to his father and those supporting senior local military commander Zahir Nayebzada, police said. The clashes have reportedly killed up to 100 people.
A spokesman for Herat governor Ismail Khan blamed Sadiq's death on forces loyal to Nayebzada.
But Nayebzada blamed Ismail Khan's forces for provoking the fighting by trying to take command of his division. Nayebzada said Sadiq was killed after breaking into his residence.