The NASUWT spoke out after the Department for Education and Skills published guidance this week to help schools protect pupils from hi-tech bullying.
A study for the Antibullying Alliance suggests more than one in five children had been harrassed via mobile phones or computers.
The DfES has instructed all schools to ensure they have strategies to tackle the problem in their anti-bullying policies and to monitor all on-site e-communication .
The union said the same protection should be given to staff. Chris Keates, general secretary, said: "Cyberbullying, of pupils or staff, is unnacceptable and should be met with zero tolerance."
The union said it had dealt with an increasing number of cases of cyberbullying against teachers in the past two years, including one in which a picture of a teacher's face was superimposed onto obscene images.
In another, a hate website was set up to target a teacher. In other cases, staff suffered sexual and homophobic harrassment by telephone and email.
The NASUWT and the Association of Teachers and Lecturers are involved in industrial action at St Cuthbert's school, in Newcastle, over cyberbullying. Staff voted in May to refuse to teach a pupil who took a photo of a teacher's cleavage, labelled the picture "tits" and allegedly showed it to other pupils.
Jim Knight, schools minister, said the Government would support schools in tackling cyberbullying with the same vigilance as in the playground.
Parents who permit cyberbullying could face pound;1,000 fines or compulsory parenting classes - like other parents who fail to tackle their children's poor behaviour.
A poll of nearly 100 secondary pupils in London by researchers at Goldsmiths college found girls were more likely to be victims of cyberbullying than boys and that a third of victims did not tell anyone.
The study that found most of the incidents occurred out of school and that students felt that threatening telephone calls or victimisation using video-phones were worse than traditional types of bullying.