The weakness in sterling and the decline in tourism to Turkey have also hit the Glasgow-based business.
“Accordingly, profits for the current year will not meet market expectations,” said the group in a trading update.
However the business is continuing to pursue the development of a project on the Cavo Sidero peninsula in Crete, which will include a number of small to medium sized hotels “of extremely high standards”.
A court hearing of the appeals against the issue of the Presidential Decree remains scheduled for September 16 and Minoan is hopeful of a "positive decision".
Minoan said its travel and leisure division had seen a gross profit increase of 19% in its interim results, in July.
The group said continued organic growth has seen an increase in gross profit by around 19% to £3,544,000 from £2,981,000.
In the update the business said: “In overall terms, the Brexit vote, including the decline of sterling together with the ongoing situation in Turkey where tourism is down by 40%, has had a material effect, in particular in our market for late holidays, due to the reduced availability of less expensive product.
“In the past few months the impact on gross profit has been running at approximately £100,000 per month.
“While this will have a significant effect on profitability in the current financial year, the board is encouraged by the trend in forward bookings for 2017 which show a return to a rate of growth ahead of current market indicators at 8%.”
The firm concluded: “The Brexit vote, its associated effects and the situation in Turkey will have an as yet unclear but significant impact on the financial results for the current year.
“All the indications are that this effect is temporary in nature and that the outlook for future growth is healthy.
“The board is looking forward to the hoped for early decision by the court [on the Greece project] and better trading figures as indicated by current bookings.”