According to Aljazeera's correspondent in Kandahar, Mazin Aman Allah, a bomb which had been placed on a bicycle behind a parked car exploded in a crowded market square. Both were destroyed in the blast at about 08:30 GMT.
The blast destroyed several shops and shattered windows in nearby stores and hotels.
The area is home to many government offices.
City police commander Muhammad Hashim blamed the attack on "the enemies of the government", referring to Taliban fighters who continue to wage a campaign in the south and east of Afghanistan two years after their ouster.
All the injured were believed to be Afghan civilians. Five people were seriously wounded.
At least two people in the car were seriously injured when the bomb exploded, witnesses told AFP.
Debris from the explosion littered the road, which was splattered with blood. US troops arrived shortly after the explosion.
Kandahar provincial governor Yusuf Pashtun said the bombers' "only intention is the destruction of Afghanistan".
This is the third blast in less than a week in the city, a former stronghold of the ousted Taliban.
"Their (the bombers') only intention is the destruction of Afghanistan"
Provincial governor, Kandahar
The police chief said the latest incident followed an explosion on Wednesday evening in fields next to the headquarters of the International Security Assistance Force and US embassy in Kabul.
No one was injured and the cause of the blast is still being investigated.
On 11 November, a car bombing at the main UN compound in Kandahar injured three Afghans.