Education Minister Peter Peacock has said he is "very surprised" that any school might cut courses to help pay for a new teachers' pay package.
Financial pressures could see exam choices being cut
Highland Council has warned that the pay deal means schools may have to prune their existing curriculum.
Chris Oughton, a senior pupil at Millburn Academy, Inverness, said the loss of Advanced Higher options would jeopardise academic prospects.
Mr Peacock said schools had been given extra money to fund more teachers.
The new pay and conditions deal, a key part of the McCrone agreement, will see staff spending about an hour a week less actually teaching classes.
The Scottish Executive identified additional funding for the implementation of the agreement. In Highland Council, the allocation is £769,000, according to the authority.
Highland Council's director of education Bruce Robertson said: "If we were to give every school in Highland an additional hour for each teacher, the total bill would be £2.7m and in the case of secondary schools, £1.4m.
"It is clear therefore that we are not in a position to allocate additional funding to all schools for this purpose."
Primary schools had "little flexibility" in staffing levels and had to be the council's first priority for the extra money to meet the 22.5 hour class contact week for teachers and this was where the entire allocation would be spent.
Mr Robertson went on: "The decision to reduce curriculum options such as Advanced Highers is entirely within the schools' decision-making process and the council has not taken a decision to cut Advanced Highers in schools.
"The reality, for most schools, is that these are courses which attract very small numbers of pupils and it is understandable that they are looking at hard choices in the senior school."
The council would be meeting secondary head teachers in the next few days to discuss the issues.
But Mr Peacock, who is a Highlands and Islands list MSP and a former leader of Highland Council, said teaching costs had been exempted from efficiency savings in grants given by the executive to councils specifically to allow them to increase teacher numbers.
He had just given Highland Council an extra £2.6m over the next two years, through a formula agreed by the Convention of Scottish Local Authorities, for extra teachers.
"I'm very surprised therefore to hear that any school might intend to cut courses," Mr Peacock said.
"It is particularly surprising that this should happen at a time when we are seeing more and more staff entering schools.
"In addition to the extra cash we are giving to employ extra teachers, this year alone, Highland has been given over 100 new probationary teachers."
Referring to the Millburn Academy example, Mr Peacock said he was in "no doubt" that the head teacher would be explaining why the decision had been taken.
"While it is for individual schools to decide what courses and subjects to offer, schools' actions are monitored by councils and they look at the choices and options that schools present for their pupils as part of that process," he added.
The council said money was at the heart of its decision
Mr Oughton, who is a representative on the executive of the youth parliament Highland Youth Voice, said the reaction amongst pupils had been one of "outrage".
The 16-year-old from Inverness said: "Sitting Advanced Highers gives pupils a competitive edge, it's up to the Highland Council to provide such services and to scrap them is a rash decision.
"A few schools have set up petitions and we are lobbying MSPs and councillors to apply pressure.
"We will be at a disadvantage when it comes to sixth year and we are applying for university against others who have had the opportunity to sit Advanced Highers," he added.
Responses to petitions set up have included concerns that it could harm the prospects of students seeking to apply for highly competitive courses like medicine and veterinary medicine and that it was reducing equality in the Scottish education system.
The Scottish Socialist Party MSP and former teacher, Rosemary Byrne, backed the pupils and said Highland Council's decision was "robbing Peter to pay Paul".