Samim Khpolwak, spokesman for the provincial governor in Kandahar, says the attack took place yesterday evening at the police headquarters in Arghistan district.
Khpolwak says the police chief, Abdul Manaf, and two policemen who served as his bodyguards died in the explosion while six other policemen were wounded.
Taliban spokesman Qari Yousef Ahmadi claimed responsibility for the attack in an email sent to media.
The violence comes amid the Taliban annual offensive during the fair spring and summer weather. The offensive is aimed at undermining the Western-backed government as foreign combat troops prepare to withdraw by the end of the year.