Brooks, an alumna of the London College of Communication (LCC), was awarded the fellowship last year.
Today the local branch of the lecturers' union the University and College Union (UCU) wrote to Rector Nigel Carrington calling for the award to be revoked.
This follows a series of allegations of criminality against the Sunday tabloid, in relation to phone hacking and the payment of police officers for information, and this weeks announcement that the title will close this weekend.
Chair of UCU Gary Horne said the call for the honorary fellowship to be withdrawn was "based on the reaction from staff and the general public to the reprehensible and repugnant activities recently detailed about the activities of the News of the World and some of its journalists."
Horne, who has previously worked for First Tuesday at ITV and BBC's Panorama, is course director of the MA in Journalism and was recently elected a governor at the University of the Arts London (UAL), of which the LCC is part.
He added: "This was a culture that was presided over by Rebekah Brooks (Wade) when she was editor and as many have already stated she should take responsibility for this."
He said the concern among staff at the long-established college is that the association could tarnish its reputation.
"We run our own highly successful journalism courses which embody clear public service values and teaches young students to practice all the journalism ethical codes of conduct," Horne added.
This morning head of college Sandra Kemp emailed all staff alerting them that "following discussion in the media and social media about the News of the World situation, a number of LCC staff have been approached for comment by journalists".
The email goes on to say that "it would be inappropriate for us to comment on any aspect of this matter while official investigations are ongoing" and warns staff they should refer media calls to the college press office.
A statement from the UAL press office said the university bestows honorary degrees and fellowships upon people it judges "to have made considerable contributions to the creative and cultural industries".
"In 2010 Rebekah Brooks, an alumna of the university, was presented with an honorary fellowship in recognition of her achievements in journalism and the media, which include her appointment as the Sun's first female editor in 2003 and her work as a founder member of the organisation Women in Journalism.
"It would be inappropriate for the university to comment on allegations about the activities of the News of the World while police investigations are ongoing."