Asadullah Khalid, the governor of Kandahar province, said: "The suicide attacker detonated near a Canadian military convoy. In the attack 35 civilians were killed, 27 civilians were wounded and also three Canadian troops were wounded."
On Monday, thousands turned up to bury friends and relatives who died in the Kandahar blast, described as the deadliest since the Taliban was driven out of power in 2001.
Khalid 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.
Meanwhile, the British ministry of defence said that one of its soldiers was killed on Sunday in another explosion in the southern province of Helmand.
The soldier was killed and another wounded when they were caught in a blast while on foot patrol in the Kajaki area
Sixteen international soldiers have been killed in Afghanistan this year.
Most of them were US nationals, but the toll includes Canadian, British, Dutch and Italian troops.