The off-duty policeman, 47, was stationed at Mbizeni police station, Colonel Sibongile Soci said.
The policeman was visiting a local tavern when he and another man got into an argument. The policeman left the tavern and drove to a supermarket, but the man he had been arguing with followed him there.
The man allegedly shot the policeman, who died at the scene, and soon afterwards handed himself in to the police.
He would appear in the Matatiele Magistrate’s Court soon to face a charge of murder.