The University and College Union (UCU) is calling for the "stay at home" message to be applied to universities.
The union is urging the Scottish Government to provide guidance stating that students and staff - including those at St Andrews - can work remotely until the end of the current semester.
UCU’s Scotland official Mary Senior claims it is "bizarre the current rules allow teaching and learning on campus" when schools across the country are closed.
She added: "The Scottish Government needs to do all it can to limit travelling and mixing of students and staff, and so must regrettably put all learning and student support online for the time being and for the whole of this term.
"We saw in September and October the significant outbreaks on campus when students and staff returned for the autumn term.
"We cannot allow this to happen at this perilous stage of the pandemic."
Currently students have been told not to return to campus until in person teaching resumes.
However, many students are still having to pay rent for their term-time accommodation.
Matt Crilly, president of the National Union of Students Scotland, says it is an "unfair" situation - and has called on the Scottish Government to help out.
Holyrood originally planned a staggered phased return for his month, allowing students to return over a six-week period with Covid testing available.
A Scottish Government spokesperson said: "We are looking urgently this week, working with universities, unions and student representatives, as to whether any further changes are required to the planned staggered return for university students."
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