The tribunal could also silence cyber bullies by issuing "take-down" orders.
A new criminal offence for publishing offensive comments on Facebook and Twitter and sending hurtful text messages would also be introduced under the Law Commission proposals.
The measures are in a ministerial briefing for Justice Minister Judith Collins, released today, as part of a Government crackdown on internet nuisances.
Prime Minister John Key called for a "national conversation" on reducing bullying in schools after cellphone videos of children being attacked went viral last year.
Fifteen-year-old Wanganui schoolgirl Robin de Jong was filmed being kicked unconscious by a classmate, who was later expelled.
In May, the Minister asked the commission to fast-track its report looking at ways of reducing harm caused by cyber-bullying.
The Communications Tribunal would operate like a "mini-harassment court", specialising in digital communication, project leader Prof John Burrows said.
It could issue statutory orders including cease and desist notices or orders requiring retractions, apologies or rights of reply. It could also reveal the identity of offenders, via the media or in its decisions published online.
Prof Burrows said the tribunal would be headed by a district court judge, who would be supported by an IT adviser.
Complaints would first be referred to an approved agency such as Netsafe, as they might be settled with mediation.
For serious cases, alleged offenders could be charged under the Summary Offences Act for publishing material that is "grossly offensive or of indecent, obscene or menacing character or knowingly false". The law would apply to anyone over the age of 14 and carry a penalty of up to three months' imprisonment or a fine of $2000.
"There are laws under the Crimes Act, like threatening to kill someone, which can be applied to anything," Prof Burrows said.
"But it doesn't deal specifically with the internet and as technology grows, we want to patch up any existing gaps."
The offence exists in Britain and 25-year-old English man Sean Duffy was jailed for four months last year after leaving hurtful messages on a tribute page for a 15-year-old schoolgirl who committed suicide.
The commission is also looking at amendments to existing offences under the Crimes Act. At present, the charge of inciting a person to commit suicide applies only if the victim has committed or attempts suicide. But the proposed law could see a person charged regardless.
The offence of publishing intimate photos or recordings without consent applies only if the photos were taken without consent. But the amendment would see a person charged, even if the victim had given consent.
The commission has also recommended schools be legally required to implement policies around cyber-bullying, including guidelines on how they deal with incidents, and educational programmes for students. It would be up to the Ministry of Education what sorts of policies would be set out.
The commission received about 60 submissions, including one from the Post Primary Teachers' Association that said there was a lack of clear and authoritive channels for dealing with serious complaints.
President Robin Duff said although some social media sites had channels to have offensive material removed, it often took days and apologies were not easily sought.
The commission proposed that principals, police and coroners have direct access to the tribunal.
"Not only does it provide a forum whereby victims of online harassment can get assistance but, in the long term, it may well lead to a change of attitude and the development of more positive behaviour around internet use," Mr Duff said.
Ms Collins welcomed the recommendations last night.
"We must not underestimate the devastating impact this new form of bullying has, particularly on young people. It is contributing to increased truancy, failure at school and emotional problems, such as depression, self-harm and suicide," she said.
