New national regulations mean that teachers can now claim full holiday pay while they are signed off sick or on maternity leave.
Until now, teachers have always only claimed a maximum of ten days' compensatory leave.
It means that teachers who claim long-term sick pay would be entitled to up to 66 days' holiday pay, as a result of the long summer holidays that teachers receive.
City council officials have estimated that the cost to the already cash-strapped council will total 1.1m a year, providing a major new budget pressure, but they expect the national pay award for non-teaching staff for 2010/11 to be lower than the one per cent rise they have budgeted for, which could help ease the impact on finances.
Donald McGougan, the council's director of finance, said: "There will be a cost each year to the council for the additional holidays which teachers can now accrue when returning from maternity leave and sickness and absence. Provision will be made for this in our budget-setting process. The estimated cost is 1.1m"
He described the new pressure as "a very difficult change to deal with", but in advice given to councillors ahead of the 2010/11 budget, he said they should estimate non-council workers will only get a 0.7 per cent pay rise, 0.3 per cent lower than original estimates, which could help meet the new cost.
"It could be possible to reduce (the estimated pay award] to the figure of 0.7 per cent, which would compensate in terms of the teacher figure," said Mr McGougan."
The annual pay award for council staff is negotiated by the Convention of Local Authorities (Cosla) on behalf of Scottish councils, so the city council cannot insist on the pay rise being lowered.
The changes to teachers' holiday entitlement comes as a result of rulings in the European Court of Justice and the House of Lords.
Unions say they have not campaigned for the changes.
Colin Mackay, the Edinburgh branch secretary of the EIS teachers union, said: "I feel sorry for the council that, at a time when they need to make savings, an additional pressure has been added as a result of primary legislation."
Councillor Iain Whyte, leader of the Conservative group on the council, said: "Nobody disagrees that some holiday pay should be added in but it seems out of all proportion to get up to 66 days when someone is already on maternity leave or sickness leave."
A spokesman for Cosla said: "We are aware of the teacher issue but it is a UK regulation.
"It will affect all employees in the private and public sector."