The suicide bomber killed 12 Nato troops and four Afghan soldiers, a Taliban spokesman told the Reuters news agency in Pakistan by telephone.
There was no independent confirmation of the report.
Kandahar is considered to be the heartland of the Taliban and is near Helmand where US marines are engaged in a major assault against the Taliban.
The province supplies most of the opium poppy funding the Taliban's activities.
The US marines are the biggest wave of 17,000 fresh US troops ordered into Afghanistan by Barack Obama, the US president, as part of his strategy to defeat the Taliban.
The US-led offensive in Helmand, code-named Operation Strike of the Sword, was launched last Thursday.
While no major battles have been reported, attacks there and elsewhere have killed civilians as well as Afghan and foreign soldiers.