They have contacted Edinburgh Napier University to complain about taking on a lecturer in child and public protection for the School of Nursing, Midwifery and Social Care on such a basis.
The post, currently being advertised on the university's website, requires candidates to have an "approach that is flexible, resourceful and innovative" as well as "excellent interpersonal skills" and the "ability to display sensitivity and to support students and colleagues in an area of study that can be emotionally demanding".
The University and College Union (UCU) has been campaigning against the use of zero-hour contracts in the sector and has raised the issue with Edinburgh Napier University principal and vice chancellor Professor Andrea Nolan.
UCU Scotland official Mary Senior said recruiting lecturers on the controversial contracts was "an embarrassment".
She said: "Employing lecturers on zero-hours contracts is not conducive to a professional, well-supported and valued workforce.
"Students want staff who are not only on campus when the university can offer them some hourly work.
"The continued use and promotion of zero-hours jobs in the sector is an embarrassment and is damaging the reputation of higher education in Scotland."
The union has given evidence against the use of the contracts to the Scottish Affairs Select Committee at Westminster.
Zero-hours contracts are not defined in law but have come to refer to employment contracts which do not guarantee the provision of work.
While they can give flexibility to both parties, they can result in workers lacking guaranteed income and having reduced access to entitlements such as maternity, holiday and sick pay and redundancy rights, a report from the committee earlier this year found.
Committee chair Ian Davidson MP said at the time that the "overwhelming majority of zero-hours contracts are abusive and exploitative, and should be abolished".
Ms Senior has written to the university principal, stating that the "UCU has been campaigning for some time against the casualisation of the workforce".
She said: "We do not believe that employing individuals on zero-hours contracts is conducive to a professional, well-supported and valued workforce, nor does it promote a positive student experience. UCU is pleased to be working with a number of employers in the sector in Scotland to move away from the use of zero-hours and hours-to-be-notified contracts.
"I would urge Edinburgh Napier University to engage with its trade unions on this matter and to end the use and promotion of such contracts at the institution."
A spokeswoman for Edinburgh Napier University said it used such contracts "on a limited basis for around 3.5 per cent of the academic effort of the university".
She added: "We do fully appreciate the limitations of these contracts and are currently seeking to reduce our usage of these type of contracts.
"These staff are employed by the university to complete flexible and specialist short-term or unexpected academic requirements, when certain business needs arise.
"Our zero-hour contracts are not exclusive and these staff often have similar arrangements with other organisations.
"Our zero-hour staff are employed on the same terms and conditions as all other academic staff. The flexibility of the arrangement is therefore key to both the individual and the university."