In recent weeks, scores of civilians have been killed in a spate of attacks across Afghanistan.
Sunday's explosions went off in the Arghandab district, on the outskirts of Kandahar city, where NATO and Afghan forces have been working to push out Taliban and establish order.
Though dog fights are against the law in Afghanistan, they are still common and often ignored by the authorities.
In this case, however, police had heard about the fight and had just arrived to break it up when a bomb exploded, said district Police Chief Niaz Mohammad. Another blast went off as security forces got out of their vehicle, Mohammad said.
Five policemen were wounded but none killed, he said.
It was unclear who the target of the attack was, though a witness said it was unlikely that it was the police.