The city's procurator fiscal called in the police after Mr Macdonald was forced in February this year to make a public admission of gross negligence in the use of false professional qualifications.
These included membership of three professional institutes and possession of a Masters degree.
The council simultaneously accepted his early retirement.
Mr Macdonald worked for Aberdeen City for 11 years, initially as the council's director of works and more recently as its chief executive.
During that period he enjoyed considerable support from members, surviving revelations that he served two short prison terms in his youth and allegations of bullying staff.
The charge against Mr Macdonald is understood to relate to a period before he joined the council.
Grampian RC, the pension authority for Aberdeen DC, decided earlier this month to seek further legal advice about the district's decision to pay Mr Macdonald a pension from the age of 50.