Nato soldiers cordoned off the site of the attack and smoke could be seen rising from a house located nearby, set on fire by the explosion.
Most Nato soldiers based in Kandahar are Canadian.
Al Jazeera's Bernard Smith said the Taliban has claimed responsibility for the attack.
In other violence, Taliban fighters attacked a district administrative compound on Tuesday in the southern Zabul province.
The ensuing one-hour gun battle left one Taliban fighter dead and three wounded, according to Mohammad Younus Akhunzada, the district chief of Mizan.
Afghanistan has experienced rising violence over the past two years, the bloodiest period since US-led troops overthrew the Taliban government in 2001.
More than 150 people, many of them civilians, were killed in two separate suspected suicide attacks last month in Kandahar, a former bastion of the Taliban.