The National Association of Head Teachers says experience in the classroom and spending time as a deputy head are vital.
Several non-teachers signed up for trials of the National Professional Qualification for Headship which started earlier this year. Five thousand people have already been accepted for courses, with 3,500 starting them next month. A pilot course means 200 people will receive awards in March.
The two-year NPQH is the centre-piece of a drive by the Government to improve standards of management in schools.
The NPQH will form the basis for a new qualification the Government plans to make compulsory for all new headteachers by 2002.
The move to open up training in headship to non-teachers also follows fears over a looming recruitment crisis in schools.
The position of someone from a non-teaching background applying for a headship after successfully completing the the two-year NPQH is yet to be tested.
But the DFEE said it was up to governing bodies to make appointments and there would be nothing to stop them employing a non-teacher as long as the post did not involve teaching. It is thought there may be some big secondary schools happy to recruit a non-teacher to improve school management.
David Hart, general secretary of the National Association of Head Teachers, said recruiting from outside the profession was unacceptable. "Unless you have proved yourself as a good quality teacher it is extremely difficult to expect a person to lead a school. Running a school is not simply a management job. You can have all the management skills in the world, but unless you've had experience as a teacher it's very difficult to expect someone to take on the role of a head."
A spokesman for the Teacher Training Agency said: "We have candidates on the trials from a variety of backgrounds including educational administration and industry. The TTA is keen to attract people with the potential to become good headteachers who lead and manage the schools of the future."
The DFEE said: "The Government would not want to deter potential candidates who might bring valuable skills from other fields of employment from training as heads. However, achieving the NPQH is no guarantee of employment. That would be the decision of the school's governing body."