However, Mr Morrison encouraged a policy of “social distancing” amongst children, where they stay 1.5 metres apart from each other at school.
Speaking after a special national cabinet meeting on Sunday, Mr Morrison said shutting schools down would do more harm than good in stopping the spread of coronavirus.
“People are naturally anxious about the issues of schools,” he said.
“As the British chief medical officer observed over the last couple of days, the issue of wide scale closure of schools, and it may seem counter-intuitive, but the advice is this could be a very negative thing in terms of impacting on how these (epidemic) curves operate.”
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Even though schools are staying open, Mr Morrison said students were to socially distance themselves from each other, which means staying 1.5m apart.
“It’s pretty straightforward,” he said.
“You are (to stay) about 1.5m away. Ensuring that you refrain from that sort of physical contact, whether it might be a handshake or something a bit more intimate, unless my close family and friends. It’s all commonsense.
Mr Morrison said the government didn’t want to leave medical workers looking after their kids rather than coronavirus patients.
The Prime Minister added that taking kids out of school could lead to more infections as they engaged with the broader community.
“So while it may seem counterintuitive, there (are) very good reasons why you would not be moving to broadscale closures of schools,” he said. “That could make the situation worse, not better.
“The states and territories are not moving in that direction.”
Mr Morrison said the matter would be reassessed on Friday.
“We don’t need to tell Australians how to get out of bed in the morning and put their shoes and socks on and things like that.
“Australians understand, these are important, normal, social interaction measures that people can take … and all about reducing the amount of direct physical contact you have with others.
“I would expect teachers or those of preschool or in churches or wherever (to follow this).
“I got a message from my church during the course of the week after Friday and they were putting measures in place and good for them.
“School clubs and others are doing the same thing.”
European countries had different ideas, with Spain announcing the closure of all schools, universities, restaurants and other non-essential places last night.
Italy and France have already gone into lockdown.
There are increasing calls for Australia to do the same.