Incidents reported by the 1,362 heads surveyed in England, Wales and Northern Ireland included being punched, spat on, kicked, head butted, bitten and sexually assaulted.
Twice as many reported being victimised on social networking websites.
The government said attacks on teachers were "completely unacceptable".
About 1,300 of the NAHT's 28,000 members in primary and secondary schools took part in the survey.'Unacceptable pressure'
One respondent described a "serious kicking attack" that left its victim "badly bruised" and with "difficulty walking for a couple of days".
Another said a table had been thrown at them. There was one case where a head teacher said a parent had tried to run them over in a car park. And one description read: "Punched in the face, bitten, kicked, spat at, hand down T-shirt to grab breasts, hair pulled."
Almost 75% of respondents said they had suffered verbal abuse or threats from a parent in the past five years, and 86% said parents' behaviour towards teachers had worsened.
National Association of Head Teachers general secretary Russell Hobby said: "School leaders often have to make difficult decisions about discipline, exclusions, holidays and the distribution of limited budgets.
"Many come under unacceptable pressure designed to effect undue influence on them. All are dedicated to doing what is best for the children in their care. Some pay a high personal cost for this dedication."
But he also said "the vast majority of families" were "a pleasure to work with".
A Department for Education spokesman said: "Violence against staff by parents or pupils is completely unacceptable. A physical assault against a teacher is a criminal offence and we support schools in working with the police to take firm action where needed."
The report comes about a week after a survey by the Association of Teachers and Lecturers, in which about a quarter of those surveyed said they had been bullied by another member of staff.
Among the teachers who felt they had been bullied, 50% said it was by a senior member of staff, compared with 25% by pupils and 23% by parents.
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