Philip Lowe also confirmed the bank has contracted the troubled consultancy giant to assist it in correcting staff underpayments.
He told a parliamentary committee the central bank had discovered it was incorrectly paying entitlements when employees left the institution.
Dr Lowe said the bank was in the process of fixing the underpayments with the help of PwC, which it contracted late last year.
This would have been before the confidentiality breach scandal first came to light early in January 2023.
The consultancy firm has come under fire following revelations staff shared confidential tax information from the Treasury department.
The Australian Federal Police are investigating the leak.
Dr Lowe said he was "appalled" by the revelations.
"The use of private information of this sort for commercial gains is wrong," he said.
"It destroys trust ... it's unacceptable.
"It should come with very serious consequences for those who did the wrong thing."
The governor said the bank had one ongoing agreement with PwC for audit and risk management services.
"We're continuing to use them for that purpose and because the cost of having to change isn't worth the benefit we would get from that," he said.
Dr Lowe confirmed the bank would not take out new contracts with the firm until "a satisfactory response has been forthcoming".
"And a satisfactory response includes both complete transparency and accountability for those involved, and we will not be seeking further services until that happens," he said.
Greens leader Adam Bandt challenged Prime Minister Anthony Albanese in parliament to refer the matter to the new National Anti-Corruption Commission, which is due to start working in July.
Mr Albanese said the confidentiality breaches were "an absolute scandal", which is why the matter had been referred to the AFP.
"So it's gone well beyond the step that the member suggests, already," Mr Albanese told parliament.
He said the breach did not arise as a result of an "active procurement or Commonwealth contract", but steps were being taken to strengthen government systems.
"Secretaries have been reminded that ethical behaviour must be taken into account as part of the value for money assessments which underpin decisions under the procurement framework," Mr Albanese said.
"These revelations are indeed shocking but they do point towards a policy failure as well, and that is what the government is addressing."
Earlier, Environment Minister Tanya Plibersek said her department had a small number of PwC contracts.
"I've asked the secretary of the department to meet with PwC and make sure that there are strict controls around those contracts to ensure that they're being done in an ethical way," she told ABC Radio.
Ms Plibersek took aim at the coalition for its broad use of consultants while it held power.
Opposition finance spokeswoman Jane Hume defended the use of consultants under the previous government.
"The Commonwealth can't do everything on its own," she said.
"There will always be opportunities or necessity to appoint contracts with the big consultants or other experts in the field."
