The Melbourne university owes 1699 employees $2.6 million while 114 people employed at its privately owned college are owed almost $250,000.
The university reported what it called "unintentional underpayments" to casual workers between 2017 to 2023 to the Fair Work Ombudsman.
Casual teachers, research assistants and lecturers are among those affected, Vice-Chancellor Professor Pascale Quester said in a letter to staff.
"I sincerely apologise" Professor Quester said.
"The underpayments were unintentional but should not have occurred.
"The University and Swinburne College are ensuring that full remediation, together with interest and superannuation occur as soon as possible."
She said accounting firm KPMG had calculated how much was owed to each worker and those affected would be contacted this week.
The National Tertiary Education Union's Swinburne branch president, Julie Kimber, said the union had raised concerns about underpayments in 2022.
"Those responsible must be held to account," Dr Kimber said.
"A voluntary self-report should not be a get-out-of-jail free card."
The union claims across the nation universities have underpaid workers by more than $170 million.
National president Alison Barnes said the situation was "infuriating and unacceptable".
"The explosion of insecure work and broken governance system is fuelling the systemic wage theft plaguing public universities," Dr Barnes said.
Last week, James Cook University flagged with the Fair Work Ombudsman that some casual workers might be owed money.
In 2023, the University of Wollongong said it owed $8 million to about 6000 staff and in 2022 the University of Melbourne back paid $22 million to about 15,000 current and former staff.
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