SYDNEY - Several Australian schools and a university have temporarily closed after COVID-19 was detected in students and staff, as cases across the country rose to well over 100.

The Southern Cross University (SCU) closed two of its campuses on Wednesday after an international staff member who had been visiting from overseas tested positive.

As of Wednesday morning there were at least 112 COVID-19 cases detected in Australia, according to the Federal Health Department.

Health officials in the state of New South Wales confirmed an additional 4 cases of the virus on Wednesday, taking the total there to 64.

SCU closed two campuses -- in Lismore northern NSW, and in the state of Queensland's Gold Coast -- representing the first instance of the disease to affect regional Australia.

"A staff member reported to the University yesterday that they have been diagnosed with COVID-19 upon their return to the Philippines on the weekend," SCU Vice Chancellor Adam Shoemaker said in an online statement.

Students were told to study from home, but were not required to self-isolate as they were considered "extremely low risk."

Meanwhile, at least two high schools were closed in the state of Victoria where health officials confirmed three new cases, taking the total to 21.

A male teacher at one of the schools had flown from the United States to Melbourne and taught lessons for half a day while infectious.

Another school had a senior teacher test positive after also returning from the United States on a different flight, and closed its doors on Tuesday with the school's principal addressing students in an "online assembly" the next day.

"I guess this is welcome to our first online assembly. Clearly this is a distressing time for everyone and a very challenging period for us to work through," the school's principal said in a video posted online.

"Look after each other, stay connected, use the amazing technology that we have to support your learning over the coming days."

Victorian state Premier Daniel Andrews warned of stricter measures to slow down the spread of the virus which he said was likely to escalate over coming months.

"It remains the case that we can with certainty foreshadow extreme and widespread disruption," Andrews told reporters

"Big challenges for our economy, for schools, for workplaces, for major events, but it remains the case that that is not now. It's not a matter of panic or wanting to scare people, it's simply a matter of being as honest and upfront as we can be."