Abdul Wasi Basil, spokesman for the governor of Kunduz province, says the target of the attack was a district police chief, who was wounded in the blast.
The explosion, in Imam Sahib district, killed the police chief's brother and driver, and wounded his son.
No one immediately claimed responsibility for the attack.
Roadside bombs have been a weapon of choice for Taliban insurgents for many years, and are often used to target officials and members of the security forces.