Zia Durrani, spokesman for the police chief in Kandahar, said that Abdul Wadod Jaju died of his wounds hours after the bombing.
Durrani said that Jaju was a police commander in Kandahar city. He added that first he was injured and later died in the hospital.
Taliban spokesman Qari Yousef Ahmadi claimed responsibility for the attack.
The violence comes as the Taliban has launched their annual spring offensive, promising to step up attacks against Afghan security forces in a bid to undermine the Western- backed government as foreign combat troops prepare to withdraw by the end of the year.