Haileybury, Caulfield Grammar, Waverley Christian College and Methodist Ladies College were among other schools that contacted parents.
Lauriston Girls’ School also reassured parents the school was in regular contact with authorities.
The state education department says only students who have contracted the virus or come into contact with a confirmed case need to stay away from school.
More than 200,000 Chinese students are currently studying at Australian universities many of whom have travelled home for Lunar New Year.
Michael Hester from the Australia-China Youth Association said the group was in regular contact with about 100 students who are “very much in the dark at the moment”.
“We’ve got a support group for students who are trying to get their heads around their visa and study requirements because they have to be back in Australia by the start of the semester, which for many isn’t possible at the moment,” Mr Hester said.
He is concerned Chinese students will be viewed as “dirty” or treated differently on Australian campuses.
“So we’ve been doing a lot of promotion within our WeChat groups that it’s a medical issue and shouldn’t be put on international students,” he said.
There have been 80 confirmed deaths and nearly 3000 confirmed cases of coronavirus in China, with three cities in Hubei province, including Wuhan, locked down indefinitely since Thursday.
The fifth coronavirus case in Australia – a 21-year-old University of New South Wales student – was confirmed on Monday. In Melbourne, a Chinese national in his 50s is in quarantine with the virus.
Melbourne’s Xin Jin Shan Chinese Language and Culture School has postponed the start of term by two weeks.
Principal Kevin Hu said one student and a staff member are in Wuhan. “We are following the situation closely, watching the developments … then we’ll follow up and make a decision,” Mr Hu said.
Meanwhile, Elite boys’ private school Scotch College contacted parents on Sunday, saying it was “aware of concerns regarding the spread of novel coronavirus”.
It has advised any students who visited Wuhan or surrounding cities in the school holidays to wait 14 days after returning to Australia before they attend school again.
“We appreciate that there may be families who are travelling, or have travelled, within China during the holiday period,” principal Tom Batty wrote.
“The containment of such a virus is dependent on individual behaviour. Accordingly, we would ask you to consider whether you should delay your son’s return to school.”
In a letter to parents, Firbank Grammar principal Jenny Williams said students who travelled to China during the holidays and have symptoms such as a fever and cough should avoid attending school.
“Students who do not fall into one of the [at-risk] groups but have travelled to China will be monitored on a daily basis by Firbank health staff,” it reads.
However for state school students, only those who have a confirmed case of coronavirus or had close contact with a confirmed case in the past 14 days have been advised to stay away from school.
Experts, including Chief Medical Officer Professor Brendan Murphy, met on Monday to decide the advice to schools and parents.
Sue Bell, president of the Victorian Association of State Secondary Principals, said many principals would have their coronavirus response as their “number one priority” when they return to school on Tuesday, one day before students.
Australian Catholic University will also advise students who visited Wuhan in their holidays to stay at home for 10-14 days.
A Monash University spokeswoman said the university “has ceased all student, staff and official university travel to the Hubei province of China for the time being”.
“Additional advice regarding the impact of coronavirus on travel, and related operational issues is being developed and will be issued progressively from [Tuesday] onwards, to our staff, students and external partners,” she said.
RMIT and La Trobe universities said they would follow health department advice. Melbourne University could not be contacted for comment.
with Rachel Eddie, Ashleigh McMillan and Emilio Lanera
Michael is a reporter for The Age.