Any decision to close schools must be accompanied by measures to support parents working in critical jobs, unions say.
Australian Nursing and Midwives Federation Tasmanian branch secretary Emily Shepherd said the union supported school closures - but that measures for critical health care staff who were also parents had to be in place.
"Our members want to make sure they're ready and able to be in the workplace and we need them in the workplace," she said.
She said school groups of no more than 10 supervised children could continue in order to accommodate the needs of health care workers and other critical workers.
"We need to be innovative and we need think flexibly, and we also need to think quickly in terms of how we're going to put these plans into place - because we know that social distancing is effective in slowing the transmission of Covid-19 and this evolving crisis," she said.
Community and Public Services Union Tasmanian branch secretary Tom Lynch said the public service would still be required during the coronavirus pandemic, especially in areas like child support services, prisons, and border security.
Full-time workers would be able to take carer's leave to be at home with their children should school's close but this is likely to create a staffing shortage, he said.
"We have to keep [public] housing running, we have to keep child services running, prisons, there's a lot of stuff that we have to keep running," he said.
"If we have a lot of people on carer's leave, there needs to be a capacity to move people from one role to another, and that's far from a simple matter."
He said some form of childcare services needed to be set up for the children of workers in critical roles.
"You could have a much smaller population in the schools and then it would be possible to practice social distancing and social isolation," he said.
"We think the best health advice needs to be taken, but everybody needs to understand that there are implications for every decision. If you were close schools, that would have a tremendous impact on the public being to access public services.
"This is a time where people will see the value of having a public sector workforce. In a few months time, we could potentially need a public sector workforce to deliver food."
A number of countries around the world have closed schools but neither the federal not Tasmanian governments have announced enforced school closures.