They predict the pound;60 million School Achievement Awards, which reward staff in schools with good and improving records, will cause disputes and trigger discrimination cases.
Governors are "panicky" about having to decide who gets the money, according to the National Governors Council.
Chairman of the NGC, Christine Gale, said: "Governors will not want anything to do with this. If they have any sense they will distribute it across the board. "Having said that, if it is distributed fairly, it can be very well received in schools."
About 7,000 schools will get the money this year. A school with 200 pupils should get about pound;6,000, and one with 1,000 on roll about pound;30,000. Guidance, at present out for consultation, gives governors the responsibility of distributing the cash as they see fit.
They can choose to give the bonus to everyone, including non-teaching staff, or to those who are judged to have made the greatest contribution to the school's succss.
David Hart, National Association of Head Teachers' general secretary, said:
"There are so many pitfalls in the methods of distribution that schools could find themselves on the receiving end of discrimination claims."
Nigel de Gruchy, general secretary of the National Association of Schoolmasters Union of Women Teachers, said: "Can you imagine if a governing body decides to give it to the science department but not the English department?" John Dunford, general secretary of the Secondary Heads Association, said the cash should be distributed equally to staff to avoid governing bodies spending hours agonising over who gets what.
The schools have been chosen by the Government on the basis of a four-year assessment of test and examination results.
Schools which have pulled out of special measures and those that have performed well in a single year compared to similar schools will also receive the pay-out.
Special schools, pupil-referral units, nursery schools and small primaries can be nominated by education directors or nominate themselves.