Students at targeted universities in England will be encouraged to take an asymptomatic test ahead of a seven-day travel window between 3 and 9 December.
Teaching will move online by that date so that they have enough time to self-isolate if needed.
But the University and College of Union (UCU) said plans appear to have been "rushed" and raised concerns around the accuracy of tests.
General secretary Jo Grady also accused the government of "gambling with the safety of staff, students and the nation."
Experts have suggested that relying on rapid tests could mean a high proportion of cases are missed with false negative results.
An evaluation by Oxford University and Public Health England workers at Porton Down concluded the Innova lateral flow test - which was used in the Liverpool mass screening pilot - has an overall sensitivity of 76.8 per cent, although it detects almost all cases among patients with a high viral load. Researchers also found the detection rate was significantly affected by the level of staff training.
The UCU said the plans for mass testing - which begins on Sunday - and the movement of students during the travel window risked a repeat of the problems seen in September.
Ms Grady said: "The flaws in Government plans for mass testing are a recipe for chaos that risk spreading the virus. Not all universities are participating in the scheme, and the government accepts that people with Covid may be told they do not have it.
"We have grave concerns over how this programme will be carried out, particularly the risk of students being told - incorrectly - they do not have Covid, then relying on their test result to travel home and spend Christmas with vulnerable relatives.
"The risk of students receiving the wrong test result increases when testers have not been fully trained - rushing these plans makes that more likely."
Ms Grady added: "By choosing to continue with in-person learning until the last-minute, ministers are gambling with the safety of staff, students and the nation, betting everything on an untried testing programme, and a mass movement of students in a window shorter than two weeks."
The UCU also called for the government to urgently provide guidance for the return of students in January so staff can plan ahead.
It has launched a legal challenge over the government's decision not to move university learning online at the beginning of this academic year.
Ms Grady said: "If the government continues to insist on in-person teaching in January students travelling back to university would be moving across the country into and out of different tiers.
"UCU is concerned that many students will have spent the holidays in high prevalence Covid areas and then move back to areas of low prevalence and mixing in households, classrooms and lecture theatres.
"University staff need to be able to plan now for how they will teach and assess students next term but by waiting until the last minute to release guidance for January, ministers are helping to sow the seeds of the turmoil we saw in September."
Additional reporting by Press Association