This comes after a photo of the two at a private party went viral, causing an online outrage.
The university has launched an investigation into the incident.
"The university... will not tolerate any form of discrimination and/or racist behaviour by any of its staff or students. The behaviour by the students in the photographs is completely unacceptable," said university spokesperson Nicolize Mulder.
Mulder said even though the picture was taken at a private 21st birthday party, because they were students at the institution, action would be taken.
"Because the students are registered UP students who by their actions brought the name of the university into disrepute, disciplinary steps against the students have been taken," she said.
The SA Human Rights Commission said it was not investigating the case as it did not receive a complaint.
"We didn't receive a complaint in this matter. We just learnt about it in the media," said spokesperson Isaac Mangena.