Zalmay Ayubi says the attack occurred Thursday in the town of Spin Baldok. Ayubi said the attacker set off his bomb in a barber shop where men also go to take baths.
Ayubi said the fatalities included a police officer and 16 civilians. An additional 23 people were wounded in the blast, which occurred around noon.
Kandahar and other southern provinces are considered traditional Taliban strongholds.