In a submission to the School Teachers' Review Body's review of the roles and responsibilities leadership, Steve Sinnott, general secretary of the National Union of Teachers, which has around 8,000 school leader members, said there was "near unanimity" among headteachers that they should have classroom experience.
England should now follow the example of Wales, where qualified teacher status is a requirement to achieve the National Professional Qualification for Headship, he said.
Although heads can in theory already come from a non-teaching background, none have actually been appointed.
The NUT's point of view, shared by the National Association of Head Teachers, contrasts with that of the Association of School and College Leaders, which accepts that a suitably qualified school manager, with previous experience in education, could take on the management of a school.
The Association of Teachers and Lecturers' position is less clear, although it recognises that the job of headteacher may now need to be split into its business and educational roles.
Joint evidence submitted by the "social partnership" group of unions, including the NASUWT, ATL, ASCL, NAHT and the Professional Association of Teachers, local government employers and the Government, added that it was "not persuaded" by the benefits of joint headship, where two people are appointed full-time to lead a school.
The use of professionals other than teachers to manage staffing and finance could allow school leaders with teaching qualifications to put their skills to the best use and achieve a better work-life balance, it said.
The Government has asked the review body to consider the changing roles, following a major report by PricewaterhouseCoopers's consultancy division, last year. Its report recommended that schools move towards new leadership models such as federations, shared headships, and distributed leadership.
It asked the Government to "endorse proactively" the possibilities of non-teachers taking on headship roles.
The review body has also been asked to look at extended schools, where schools stay open from dawn until dusk, and executive headship - issues which are not at present recognised in the pay and conditions document.
The review body will publish its report in January.