Business rates, charged on property in England, are due to change in April for the first time in seven years.
Calculations by consultancy Gerald Eve suggest changes to the rateable value of schools mean some will face 40% bill increases.
The government said its own figures suggested state schools overall would see a 2% fall in rates.
Andrew Altman, a specialist schools partner at Gerald Eve, said the firm estimates that the total rates bill for schools in England is about £791m.
But it estimates that this could rise by £131m to about £922m by 2021-22 as the revaluation changes work through.
The figures amount to a rise of about 17% by 2021, said Mr Altman, but this "hides the fact that about a quarter of schools could see actual rate increases of about 40% in the first year".
Mr Altman said he feared that council-run schools would be particularly badly hit as academies have their costs, including rates, met fully, directly from Whitehall.
He said that he expected many schools to appeal against their new business rate rises and questioned why public sector properties were subjected to business rates at all.
"It's circular. It's all public money. It's a very expensive tax to collect and appeal," he added.
National Association of Head Teachers' general secretary Russell Hobby said a sharp increase in business rates would "add to the perfect storm school leaders are experiencing.
"It cannot be right that more and more of the money to schools is being taken back to central and local government."
Mr Hobby said schools were already having to find money, which would otherwise be spent on pupils, to fund the Apprenticeship Levy which also comes into force from April, as well as staff insurance contributions and pension costs.
"The burden on schools is becoming too much," he added, urging the chancellor to "act in next month's Budget to ensure schools have the resources they need".
In a statement, the Department for Communities and Local Government said it did not recognise the Gerald Eve figures and state schools would see a 2% fall in their bills - equivalent to £16m a year.
"The revaluation of business rates means nearly three-quarters of properties will see no change or a fall in their bills," said a spokesman.
The National Day Nurseries Association said its members, who operate as small businesses, feared their business rates could double.
Research late last year by the Lambert Smith Hampton commercial property consultancy estimated rises of 45%, or higher in more affluent areas.
NDNA chief executive Purnima Tanuku said these rises would be "a huge burden" when nurseries were already facing "severe financial pressure" due to the national living wage and uncertainty surrounding the financial viability of the government's plan to double the number of free childcare hours for working families.
A sharp rise in schools' business rates could push some budgets beyond breaking point, say head teachers' leaders.