Napier Police Youth Services co-ordinator, Sergeant Alan Potter, said: "I am unaware in relation to this, but I encourage people to make a complaint - it is the kind of thing that can create big problems in kids' lives," he said.
"On Facebook and other social media, I've seen it, and it's pretty nasty stuff. This kind of thing is pretty prevalent, it's just that we don't tend to deal with it as much.
"I would encourage parents of kids being bullied to report it."
Hastings Youth Services Co-ordinator, Sergeant Ross Stewart, said he had seen serious action taken against misuse of social media. "It can constitute an offence depending on what is said and how it is said."
He had dealt with a number of cases where young people faced legal action from their activities on social media.
"There have been a couple of cases and they have been dealt with by way of diversion, mainly because of the age of the individual I think these people need to be careful about what they are putting up about others because there are all sorts of rules over civil and criminal law."
Auckland lawyer and internet safety group NetSafe chairman, Rick Shera, said internet rumours could constitute defamation or harassment, and in some circumstances bullies could face legal action.
"Yes, it could be defamation and yes, it could be harassment," he said. "People could take legal steps in civil court if the police were not interested in taking some sort of criminal action - it is reasonably common now."
Child psychotherapist at Napier Family Centre Dianne Lummis said the bullying could have serious impacts on mental health and was a growing issue.
"I think it can have a major influence on people's self-esteem and self-worth, and it is sexual harassment, isn't it?
"It is increasingly common. We have had a number of cases in the last year as young as intermediate age where they get bullied at school but then they are being bullied on Facebook as well."
Ms Lummis said it was important for parents to talk to children about bullying and social media.
"It is as serious as face-to-face bullying. I don't think all parents realise how important that world is to kids, because we hardly go on it. But it is just as important."