"[Ken Sinclair] was suspended yesterday [Monday] and won't be attending classes," said spokesperson Thami Nkwanyane.
This was pending the outcome of a disciplinary process.
The City Press website reported that Sinclair posted a message two weeks ago in which he said black people were "fucking brain dead monkeys [who] always skinner [gossip] in their retarded language".
Nkwanyane said CPUT condemned Sinclair's actions in the "strongest possible terms".
The matter was an isolated event and not representative of the mindset of Cput students, he said.
It was not clear how long the disciplinary process would take to complete or what penalties Sinclair could face if found guilty.
Racism on social networks made headlines recently when two models, Jessica Leandra dos Santos and Tshidi Thamana, apologised after public condemnation of racist Twitter posts.