The incident happened in Lora village, 80km (50 miles) south of Abbottabad.
Reports said the landowner Mohammad Miskin, who denies the charges, became angry after animals the boy was looking after strayed on to his land.
He tied the boy to the donkey and beat it to make it run faster, witnesses said. The boy, an eight-year-old named Mudassir, died of his injuries.
Local villagers contacted by the BBC said the landowner assaulted the boy after his small flock of sheep and a donkey strayed on to his agricultural field.
"He tied up the boy, and then tied him to the donkey, and then he made the donkey run," one villager said.
Local people say the donkey dragged the child for nearly an hour.
"My child was murdered ruthlessly," his father, Sher Afzal, told the BBC's Mohammad Zubair Khan. "Instead of intervening in the matter and saving the child's life, people were searching for me.
"When I arrived at the scene, the boy was already dead. There wasn't a single part of his body which wasn't bruised."
Mohammad Miskin denies the allegations against him. "I didn't tie the boy to the donkey," he told journalists. "They came into the field and I just shooed them away."
A court in Abbottabad has remanded him in custody for two days for further questioning after his arrest on Wednesday.
Police in Pakistan have arrested a man accused of tying a young boy to a donkey which then dragged him to death.