The 13-month-old Basset, known as Bismarck, died shortly after the shooting on Friday morning.
Owner Hennie De Jager said two of his dogs had gone out of his yard around 06:30.
“The dogs ended up on my neighbour’s property. He chased them and cornered them and fired four times. Bismarck was hit three times,” he said.
De Jager said the man left Bismarck to die slowly.