The man, his 12-year-old daughter and his 13-year-old nephew, were killed instantly when the cart struck the mine in the country's northwestern Oddar Meanchey province, local police chief Keo Tann told AFP.
"The explosion happened when their cart, which was carrying wood from the jungle, ran over an old anti-tank mine from the civil war time," he said.
The area was the site of fierce fighting during the civil war between the government and Khmer Rouge forces, he added.
In 2012 leftover land mines and other unexploded ordnance killed 43 people and caused 142 injuries, according to official statistics.