Nearly all classes at the border's two university campuses have, or will, switch to online delivery.
Both TAFEs are going ahead with face-to-face teaching, altered in line with health advice, but Wodonga TAFE chief executive Phil Paterson said it was a rapidly-changing situation.
"While at the moment the TAFEs remain open, obviously that's subject to change and that depends upon a number of factors including the spread of the virus and advice from government," he said.
"The challenge is, there's probably only certain amounts of our content we can put online and there's a practical element to our training
"We're making sure that any training we're delivering on campus has social distancing guidelines in place."
Mr Paterson said online teaching was happening where possible and a strategy would be devised if TAFEs were closed.
"I think some courses probably have a degree of flexibility in terms of the timeframe," he said.
A spokeswoman for TAFE NSW said the Albury campus had implemented a range of social distancing measures in face-to-face delivery, including by reducing the size of the classes by splitting up practical and theoretical activities.
"Teachers have also been advised to take other practical measures such as limiting movement and contact between student groups, staggering class break times and conducting lessons outdoors where possible," she said.
Across La Trobe University, 90 per cent of teaching is moving to online modules, and a financial assistance program has been created.
At Charles Sturt University Albury-Wodonga, classes began to transition to an online format on Monday.
Residential common areas will remain open and students will be required to abide by social distancing protocols.
Vice Chancellor Andrew Vann said in a statement on Monday a Charles Sturt student at an unspecified campus who had gone into isolation after returning from Italy "several weeks ago" had been a confirmed case.
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"No contact was made on campus and there has been no impact to university operations," he said.
"We have 42,000 students and it is likely more cases will be confirmed over time.
"We will publish them when we need to alert students or the community for contact tracing. Currently, no contact tracing is required.
"We have mechanisms in place to ensure continuity for our students and staff across all of our campus locations should a COVID-19 outbreak occur."