She refused to remove her hijab, insisting instead on wearing the wig on top of her headscarf, local media say.
This was deemed as going against the dress code set by her law school, the university says.
Ms Firdaus described the actions of the Nigerian law school as "a violation of her rights", according to reports.
The case has attracted significant attention on social media.
A female Instagram user said Ms Firdaus was within her rights.
According to a user Juliet 'Kego, said it was an example of sexism in Nigerian society.