The Department of Health has questions to answer over Dr Tony Holohan's new role.
That's according to Public Expenditure Minister Michael McGrath, who says a salary to be paid by the Government was not discussed.
The outgoing Chief Medical Officer is leaving his post to take up a position with Trinity College Dublin (TCD).
Dr Holohan will take up the position as Professor of Public Health Strategy and Leadership on July 1st.
However the change is an open-ended secondment, rather than a permanent move.
As such the Department of Health is to continue paying his salary of more than €187,000 - even though he will not be working there.
Minister McGrath says his department's approval was not sought for the arrangement.
"There are characteristics of this that are unusual and it could have been handled better in the sense that, when confirmation was provided that Dr Holohan was leaving the Department of Health, I think the assumption was that it was a permanent move.
"Secondments by their nature are generally temporary in nature, this particular one is open-ended in nature - which is unusual.
"So there are questions that arise there that will have to be answered".
Earlier, Health Minister Stephen Donnelly told Newstalk Breakfast: "He is staying on the exact same terms and conditions he is on within the Department of Health and obviously, had he chosen to, he could have stayed on as chief Medical Officer for many years to come; until he retired.
"I was told about the move about two weeks ago.
"It is certainly a move I support and I think it is a very good move for the country because Tony was looking for a new challenge, he wanted to stay within public service and the research he is going to be leading now in Trinity is research around future pandemic preparedness for Ireland."
Reporting by: Stephen Murphy