Government House confirmed the diagnosis on Sunday evening, saying General Hurley was experiencing “only slight symptoms”.
“He is isolating at Admiralty House and will continue to follow all health advice and directions,” Office of the Official Secretary to the Governor-General said in a statement.
“Recent close contacts have been notified. His Excellency is double vaccinated and has received his booster.
“His Excellency will conduct his official duties virtually while isolating.”
The Governor-General of Australia and the New South Wales Governor are representatives of The Queen.
News of the head of state’s infection came just hours after Government House Sydney announced New South Wales Governor Margaret Beazley had tested positive.
“Her Excellency is experiencing mild flu-like symptoms and is resting at Government House,” a spokesman said. “The Governor’s immediate program has been cancelled in line with advice from NSW Health.”
“Organisations with whom the Vice Regal couple have interacted during recent days have been notified.”
Lieutenant-Governor TF Bathurst will step in for the Governor where needed.
Her husband, Dennis Wilson, had also tested positive and both were fully vaccinated, a spokesman said.
The Governor-General and the Governor are The Queen’s representatives in Australia and NSW.