The firm had been expected to hand the £48m project over for opening in October but has conceded that this date will not be met, and the project is now facing an unspecified delay.
Problems with the project have prompted calls for an immediate overview of education capital projects in the region.
Wick Joint Campus is being constructed to replace Wick High School and Pulteneytown and South primaries by the Hub North Scotland public-private partnership group.
A council spokesman said: “Regrettably it seems unlikely that the campus will be ready to open in October, as envisaged.
“Highland Council intends the best facilities possible for children and staff, and will not accept these buildings until work is completed.
“The council is working with the contractor to determine what the earliest possible date is for completion of the whole Wick Joint Campus project, and will make further announcements as soon as possible.”
Leader of Highland Council, Cllr Margaret Davidson, has asked the chief executive for an overview of the delivery of education capital projects, to see where further improvements can be made and any problems can be avoided.
Cllr Davidson said: “During the past year we have learnt many lessons from previous projects and this has led to many improvements in project management and better reporting to elected members. However, in some of our bigger, more complex projects, we have seen issues around delivery on time and on budget.
“There will always be snagging in these big complex projects, but it is really important that there is effective communication between services in the Council, where education capital projects are carried out and where there are a number of senior officers and stakeholders who need to be informed in a timely manner when there are issues arising.
“I have also raised concerns about the performance of HubNorth at Inverness Royal Academy and Wick Campus and have requested that these concerns are addressed at the earliest opportunity.”