The 57-year-old farmer and his 24-year-old son were arrested on Monday after police were summoned to the grizzly scene near Standerton, Mpumalanga.
According to police spokesperson Brigadier Leonard Hlathi, the pair allegedly spotted the herd of goats, which belonged to another local man, grazing on their land.
"They reportedly shot three of the goats before deciding to use their two bakkies to allegedly run over the rest of the herd, ruthlessly killing them instantly," said Hlathi in a statement.
"Police were summoned to the scene and the pair was then immediately arrested, hence their expected appearance on Thursday, 27 December 2018, to answer for their alleged villainous action."
Hlathi said that the pair will face a number of charges, including malicious damage to property and cruelty to animals.
The Provincial Commissioner of the police in Mpumalanga Lieutenant General Mondli Zuma applauded police for their swift response but urged the community to try and live in harmony with each other and solve whatever challenges they face in a civilised manner.