Journalists have been reporting on decisions for some time and none have been prosecuted for doing so.
The tribunal considers cases in which teachers' registration comes under question - these matters can include more minor offences from drink driving to serious cases where teachers have come before the courts for sexual misconduct.
The teachers name may not be suppressed before the court, but the Teachers Council suppress the majority of names in decisions published on its website.
Herald on Sunday Editor Bryce Johns said in a submission the rule had not been known to media and was an attack on freedom of expression.
"The prohibition is one of the heaviest shrouds of secrecy over any statutory disciplinary body in New Zealand.
"This blanket rule turns the basic constitutional presumption of open justice and accountability on its head".
Wellington barrister Graeme Edgeler in his submission to the committee recommended it disallow rule 32 under section 5 of the Regulations (Disallowance) Act, or amend any or all of rules 31-33 under section 0 of the Regulations (Disallowance) act to better provide freedom of expression.
He said the rule allowed the Teachers Council to effectively regulate the news media.
"I do not consider that Parliament would have intended that a power to set up a Disciplinary Tribunal, and to provide rules regulating it, would incorporate a power to regulate the news media."
The council has recently decided to highlight the rules and potentially enforce them.
Johns drew parallels to the way health professions and lawyers were treated by relevant professional disciplinary tribunals.
"The disciplinary tribunals for both of these groups of professionals hold public hearings, but are empowered to close hearings, or suppress names and evidence where necessary."
He said there was no reasonable justification to prohibit the publication of all information.
Mr Lind said the tribunal had limited power to enforce any penalty for a breach of its suppression orders.
The Teachers Council is in the process of being reviewed.
The Herald on Sunday has requested the Teachers Council revisit and rescind the rule and in the meantime revert to the previous position of not seeking to enforce it.
*The Herald on Sunday is owned by APN New Zealand, publisher of APNZ