The "messes" involved in such relationships can be "educative", he said during a question-and-answer session after a lecture at Exeter University.
His remarks, which come as legislation making it a criminal offence for teachers to have sexual relationships with 16- and 17-year-olds is before Parliament, provoked controversy among MPs, teachers and parents.
In reply to a question whether teachers who had relationships with pupils had any place in the education system, Mr Woodhead said that the law barring sexual relations with those under 16 was clear, and "as adults or relative adults we have a responsibility to those who are younger than us and therefore it isn't a good idea at all.
"But I don't think necessarily that a teacher should be automatically drummed out of the profession. I think human beings can get themselves into messes and I think those messes can sometimes be experiential and educative on both sides."
Under the Sexual Offences (Amendment) Bill passing through the Commons, teachers face up to two years in jail if they have sex or "any sexual activity" with pupils under 18 at their school.
Government guidelines already warn that teachers who have an "inappropriate" relationship with a pupil are "most likely" to be banned from working in schools, even if the pupil is over the age of consent.
Nearly 200 student teachers and academics attended the lecture on education 10 days ago. Mr Woodhead said yesterday that the exchange had to be seen in context. "I don't think it is the job of a chief inspector to pontificate about these things. I was asked a question on something completely different from the topic of the lecture and I didn't think I could duck it. In most circumstances I think a teacher who has a relationship with a pupil should be barred from the profession. I would not have any problems with the new legislation."
Gary Streeter, chairman of the Conservative Christian Fellowship and MP for Devon South West, said that Mr Woodhead's comments would set alarm bells ringing: "Such relationships have to be seen as a disciplinary offence ... although teenagers think they are grown up, they are at a very impressionable age and there is a risk of abuse."
David Hart, general secretary of the National Association of Head Teachers, which opposes the Bill, said: "Most heads would regard these remarks coming from a chief inspector as extraordinary. Parents commit their children to the care of a school. They expect the school to respect that trust."
Joe Ashton, the Labour MP for Bassetlaw, who persuaded the Government to insert a measure on the issue into the legislation, said he had received a letter from a woman of 45 who had had a relationship with her music teacher at 16 and felt scarred by the experience.
"I think somebody should send Mr Woodhead a copy of the Hansard from when this was debated in Parliament and approved by an overwhelming majority," Mr Ashton said.
Mr Woodhead has become the focus of teachers' anger for his attacks on progressive teaching methods and his suggestion that 15,000 bad teachers should be sacked. More recently, he argued that national tests were unreliable and that schools were cheating to boost their results.
Teachers reacted angrily to his comments last night, but the UK's biggest parents' group was more supportive.
Patrick Tobin, headmaster of Stewart's Melville College, Edinburgh, and former chairman of the Headmasters and Mistresses Conference, said: "In a professional relationship you are answerable for your actions. There has to be a professional ethic whereby teachers - or doctors or any self- regarding profession - know that if they become involved in an intimate relationship with somebody with whom they have a trust relationship they are endangering their professional status."
But Margaret Morrissey, of the National Confederation of Parent Teacher Associations, said: "I think parents would be concerned if an older man was involved who might be divorced or have a family. But the majority would have no problem with a man who is, say, only four years older who meets socially with a sixth-former outside school."
Professor Ted Wragg, of Exeter University's department of education, said: "We lay down the law to students... making it clear that if they were so foolish as to have any kind of relationship with a pupil they would be kicked off the course. If they were in the teaching profession, they would be kicked out of the profession."Reuse content