The union said a survey of schools last week revealed more than three-quarters of schools and preschools had between one and 10 teachers away each day.
There were similarly high rates of absences among support staff.
The AEU has suggested officials declare the final week of the current term a pupil-free period.
"As a demonstration of goodwill toward fatigued educators, this break will provide much-needed time to reset in preparation for term two," the union said in a statement on Thursday.
"Words of thanks are not enough. Real measures to address workforce exhaustion are needed now."
In response to increasing case numbers, classes in some schools have been combined.
While authorities this week decided that whole classes would be sent home if 10 or more students tested positive.
The actions came as COVID-19 infections across SA spiked on Wednesday with the daily case tally of 4594 the third-highest since the start of the pandemic.
Recent modelling suggested average daily infections could top 8000 and possibly even 10,000 within weeks with a rise also in hospitalisations and deaths.
A meeting of SA's new Emergency Management Council on Friday will consider the response to rising cases as well as SA's existing restrictions, including isolation requirements and statewide mask mandates.
Premier Peter Malinauskas said he had asked for further modelling to be provided on what the impact would be on case numbers of reducing SA's isolation and mask-wearing rules.
"We want to make informed judgements," he said.
"The more information we can have, the better for my team."
18°C