The South African Human Rights Commission has launched an investigation into the inflammatory comments by estate agent Penny Sparrow and Standard Bank economist Chris Hart.
The commission on Monday said it had noted the comments, which dominated social media, saying the remarks were concerning.
Spokesperson Isaac Mangena said the investigation, which would also include Justin van Vuuren's comments calling some people "scum of the earth", could lead to further legal steps.
Formal complaints about this matter could also be laid with the Kwazulu-Natal provincial office of the commission, he said.
"It is very concerning to the Commission that 22 years into democracy there are still comments and actions that incite and promote racism. These utterances have gone viral and angered many. They open the wounds of millions who were formerly oppressed by the apartheid government."
He said they recognised that the comments did not represent the views of the majority of South Africans.
He called for those who felt aggrieved by the comments to lodge a complaint with them.
In her Facebook post, KwaZulu-Natal realtor Penny Sparrow compared black people to monkeys.
In her post, Sparrow wrote: "These monkeys that are allowed to be released on New Year's eve and New Year's day on to public beaches towns etc obviously have no education what so ever so to allow them loose is inviting huge dirt and troubles and discomfort to others."
Hart tweeted: "More than 25 years after Apartheid ended, the victims are increasing along with a sense of entitlement and hatred towards minorities... "
Van Vuuren called for the Promenade in Durban to be made private as "these animals with 13 kids" dirtied it and said it should not be enjoyed by the "scum of the nation".