Government on Thursday condemned the "racial comments" made by Adam Catzavelos.
In a video, which has gone viral, Catzavelos records himself at a holiday spot in Greece saying: "Not one k****r in sight, f*cking heaven on earth... You cannot beat this!"
"His racist comments cannot be justified and display one of the most despicable forms of racism. Government urges law enforcement agencies to take action against Mr Catzavelos," acting Government Communication and Information System (GCIS) director-general Phumla Williams said in a statement.
News24 reported on Wednesday that Catzavelos was fired from the family's business by his brother, and he has been banned from his sons' school.
"His racial comments undermine the gains made towards social cohesion, nation-building and strengthening our vibrant young democracy. It is an insult to human dignity and to the fight for freedom," Williams said.
The statement reminded citizens that the use of social media is just like any other forms of publication, and people can be held liable for the consequences for what one posts.
"Those found guilty cannot escape the consequences of posting racist comments on social media. Racism is punishable by law.
"Whilst government respects freedom of expression, the public should be responsible in how they express their views," Williams said.
According to the statement, social media should be used to promote and build peace and harmony in today's modern society. "Citizens are urged to utilise social media platforms responsibly and with utmost caution."
On Wednesday, North-West University law lecturer René Koraan told News24 that Catzavelos could face a stiff fine or worse for using the k-word.
Advocate Bongani Majola, chairperson of the SA Human Rights Commission, told News24 on Wednesday that the commission would be "pursuing the matter on its own", whether or not any formal complaints are received by members of the public.