The NUS said the University of Northampton, Northumbria University and Swansea University have already joined its campaign and it wants others to follow their lead.
The call comes as Britain's biggest payday lenders have been warned by the trading watchdog that they risk being put out of business if they fail to demonstrate that they are up to scratch.
The Office of Fair Trading (OFT), found evidence of ''widespread irresponsible lending'' after carrying out an investigation into payday lenders, including firms appearing heavily reliant on struggling customers who cannot afford to pay their loans back on time.
Pete Mercer, NUS national vice-president (welfare), said: "Students are struggling to make ends meet and this is having a real impact on their wellbeing and their education... It's great that these institutions have already joined our campaign and I hope that others will soon follow suit."
The OFT is expected to announce shortly whether or not it plans to refer the industry to the Competition Commission, which has strong powers including banning or limiting particular features of a whole market or a particular product.
"However, as the name suggests, these types of loans should only be taken as a short term bridging loan. It's vital that anybody considering taking one out has a concrete and guaranteed means of paying it back within the specified time frame."
Russell Hamblin-Boone, chief executive of the Consumer Finance Association, which represents major short-term lenders, said: "It is concerning that the NUS is denying choices to its members, who are all educated and intelligent people, without fully understanding either the short-term lending industry or the way young people are managing their finances in 2013. Payday loans are extremely flexible but that doesn't make them right for everybody. To get a loan from a reputable and responsible short-term lender you need both regular and disposable income.
"So, unless students are in work while studying, it is highly unlikely that a reputable payday lender would approve a loan or that it would be the right choice for most students. We fully support the NUS' desire to protect its students and any efforts to drive out rogue lenders, but this campaign against advertising on campus will do little to tackle bad lending practice and discredits the whole industry unjustifiably."