At least three soldiers in the convoy and six civilians were also wounded in the attack that happened on a road in the Spin Boldak town close to the border with Pakistan, border commander Abdul Razaaq said.
Assadullah Khalid, Kandahar's provincial governor, said Sunday's blast was triggered by a suicide bomber.
He blamed Taliban for the attack.
"This suicide attack was the work of the Taliban, the enemies of Afghanistan," he said.
Among the victims was Abdul Hakim Jan, the commander of a local militia that was opposed to the Taliban.
"The [dog fighting] match was going on and all of a sudden the explosion went off," witness Abdul Rahman, whose brother was killed, said.
Hamid Karzai, the Afghan president, condemned the attack from Qatar, where he was on an official trip, accusing the "enemies of Afghanistan who cannot tolerate the happiness of our people".
"Such acts are against the values of Islam," he said in a statement.
The Taliban first surfaced in Kandahar province in the early 1990s.
While the Taliban was in government, dog fighting was considered unIslamic and severely punished. It has become immensely popular since the Taliban was driven out of Kabul.