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SU is top trending on Twitter following an incident at the well-known residence called Huis Marais.
A video of the incident, widely shared on social media, shows a white student urinating on the belongings of a student of colour.
The incident allegedly took place in the early hours of Sunday morning.
In a statement, the South African Students' Congress (SASCO) alleges that a student broke into a student of colour's dorm room and urinated on his desk.
SASCO's Queen Majikijela says the university is currently in talks with the student, and relevant structures.
AlgoaFM News has since seen a short video clip of an emergency Huis Marais House Meeting held on Sunday where a student apologises for his actions both to the other student and to the university in general.The student says he knows his behaviour was wrong.
Hundreds of students gathered outside Huis Marais on Monday.
The university's student affairs director Dr Choice Makhetha says an investigation by their Equality Unit will determine whether the incident was racially motivated.
"The investigation will tell us in detail, we also have to look at all angles around this issue what motivated this because it is totally not acceptable and once, we have all the facts on the table and certain that what was said was discriminatory, we have to deal with that. We do not condone racism, sexism and when it happens, we must act decisively through the process of the university."
Makhetha says the university will provide a laptop to help the affected student prepare for his upcoming exams.
"It is important for us to ensure that the student is able to study and prepare for exams, I promised him that we will make sure he has a laptop and all the supporting materials he needs to succeed."
Stellenbosch University (SU) has not yet issued a statement on the incident.
Outraged Twitter users said the video reminded them of the so-called Reitz Four who filmed themselves in 2007 at the University of Free State (UFS) humiliating five black workers.
(Additional reporting by Caitlin Maledo and Cliff Sikho)