The investigation relates to allegations that during his interview for the post, Nick Reiter misled members about his involvement in the 'homes for votes' scandal at Westminster City Council.
Mr Reiter worked for Westminster as head of the policy unit between 1986 and 1989 under Dame Shirley Porter's leadership, when council homes in politically sensitive wards were sold.
The practice led to a damning external auditor's report and a£27 million surcharge for Dame Shirley and her erstwhile deputy David Weeks. Both are in the process of appealing.
Mr Reiter is on annual leave and could not be contacted for comment.
Shetland vice-convenor Jim Smith said the council 'does not discuss staffing matters at any level or on any appointment'.
Mr Reiter's spokesman, Association of Local Authority Chief Executives consultant Bill Miles, said he was yet to be made aware of details of the specific claims against him, but 'we will have absolutely no difficulty in defending Nick Reiter against any of these allegations.' Mr Miles will represent him at the disciplinary hearing, for which a date has yet to be set.
Mr Reiter was appointed to the top Shetland post in May, after the death of former chief executive Malcolm Green last year. Before that he had been policy director at Highland Council where he oversaw the high-profile land purchase of the Isle of Eigg by island residents.
Highland chief executive Arthur McCourt said Mr Reiter had joined the council from the former Ross and Cromarty DC at the time of reorganisation. His employment history was well known and had 'never been an issue'.
Mr Reiter had played a leading part in supporting the community of Eigg in buying the island and 'when he worked for us was an excellent officer', Mr McCourt said.
A source said Mr Reiter's predecessor had been a 'very, very strong, aggressive chief executive'. 'It could make it extremely hard for another chief executive to step into those shoes,' he said.