Tuesday's explosion was aimed at a police vehicle, witnesses and police said, but missed.
The attack came as many people in the city observed a general mourning for more than 140 people killed in two suspected suicide raids in the past two days in other parts of Kandahar province.
The area is a stronghold of Taliban fighters who are battling the Afghan government and the US-led troops operating in the country.
Taliban stronghold
In recent years, the Taliban has made a comeback, especially in the southern areas where it enjoys the most support among civilians.
An attack on Sunday killed more than 100 people, the deadliest single raid since the US-led invasion overthrew the Taliban government in 2001.
The latest attacks come as discussions are under way among the Afghan government, the US and its Nato allies on how to stabilise the country and prevent it from sliding back into anarchy.
But in light of the rising violence, many Afghans have questioned the ability of the US military and its allies to secure the country.