A Law Commission report said adolescents were particularly vulnerable to cyber-bullying, which could lead to depression, self-harm and suicide among victims.
The report's author, legal academic John Burrows, said existing laws had failed to keep pace with developments in social media and police were dealing with increasing numbers of complaints about online threats and harassment.
"Communication is different now because it can go viral very quickly and spread to a very wide audience and other people can join in," he told Radio New Zealand.
"In the school playground it's much less likely to spread widely."
Research commissioned for the report found 10 percent of New Zealanders had experienced issues such as cyber-bullying and invasion of privacy online, rising to 22 percent among 18-29 year olds.
Burrows recommended the creation of a new crime specifically aimed at cyber-bullying, making it illegal to post grossly offensive, obscene or threatening content that was aimed at causing emotional harm.
The proposed offence would carry a maximum penalty of three months in prison.
He said Britain had introduced a similar offence, which resulted in a four month jail term last year for a man who posted abusive content on a Facebook memorial page for a teenage girl who committed suicide.
"The mere fact that it's an offence enables the police to have a bit of teeth when they say: 'Look, if that happens again we will take you to court and prosecute you'," Burrows said.
He also called for establishment of a specialised online communications tribunal, with the power to issue "takedown notices" ordering the immediate removal of offensive content.
Justice Minister Judith Collins welcomed the 160-page report and said the government would consider its recommendations as a priority.
"It's time to send a clear message to cyber-bullies, your behaviour is not acceptable," she said in a statement.
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