The University of Aberdeen has been forced to repay £119,000 of grant money to the Scottish Funding Council (SFC).
It was ordered to return the funds after a review into the pay-off which was given to its former principal.
Prof Sir Ian Diamond announced his plans to retire in 2017, but his 12-month notice period only began when he had actually left his post.
The university said it had repaid the £119,000, and would "reflect closely" on the SFC's report.
Higher Education Minister Richard Lochhead said the case was "clearly unacceptable".
Prof Diamond has not commented on the report.
He became chief executive of the UK Statistics Authority after he retired from the university.
The SFC said: "We decided to review the payment made to the former principal of the University of Aberdeen because the financial statements did not appear to accord with our understanding of the principal's retirement and we were not satisfied with the university's response to our initial enquiries.
"The former principal's total remuneration disclosed in the financial statements for 2017-18 was £601,000. In addition, a payment of £60,000 was made in relation to the former principal, for 'outplacement support'."
The review concluded that the university approved a settlement agreement with the former principal "without a documented assessment of value for money and it could have identified better-value options".
Mr Lochhead said: "It is clearly unacceptable that the University of Aberdeen did not meet its grant conditions, nor the highest standards of transparency that we expect of organisations which benefit from public funds.
"I do not believe the impact should be borne by the student or staff bodies and I therefore urge the university to consider whether it can recoup these funds."
University of Aberdeen senior governor Esther Roberton said: "The university has co-operated fully with this review, welcomes publication of the report, accepts its main findings and has already repaid the £119,000 to the Scottish Funding Council.
"Court - the university's governing body - will reflect closely on the SFC's suggestion that the university may wish to consider repaying additional monies or donating to a university learning-related activity, once it has had the opportunity to fully consider the report's findings and their implications."
Asked if the university had asked Prof Diamond for the money back, she added: "No, we have not.
"Obviously the minister's made it clear that he thinks we should do that. That will be an issue for the (university) court to decide about.
"It may not be appropriate to ask him for it back but that's something we'll give very serious thought to."