The Irish National Teachers’ Organisation says the current public health advice won't allow all students to return to schools in September.
It says the two-metre social distancing rule is not physically possible in many classrooms.
Under the government's roadmap schools are set to reopen on a phased basis from September.
Right now people are being asked to keep 2 metre apart from others, which the Chief Medical Officer Dr. Tony Holohan won't recommend changing at the moment.
However, the INTO's General Secretary says this will pose big challenges for schools if it remains in place.
John Boyle says "We will probably have to have a number of plans in place: a plan for the full return of schools with all children and workers who are fit to go back at the one time, and then maybe a plan B or even a plan C - depending on the public health advice and that key issue of social distancing.
"The Minister [Joe McHugh] was absolutely right when he stated that with the two metre rule - he didn't say about us having the largest class sizes in Europe, but I suppose it's inherent in what he said - that it just wouldn't be physically possible to have all the children back together".
He says teachers will have no difficulty returning to their full classes in September if the public health advice allows it.
In two weeks' time, schools will be issued with a guideline to reopening.
Contingency plans are being examined, such as a mix of classroom and online learning.
However, John Boyle says this poses a logistical problem "It's just not simply possible in Ireland to teach small children, maybe half of the class, and to be teaching the other half in their homes at the same time."
But some schools are already planning ahead for September with sending parents new rules for online learning.
They're being warned that there will be a zero-tolerance approach to the recording of classes or publishing videos to social media
If a student is caught they could be suspended, expelled or face legal action.