Judge David Harvey, who has written a book on the internet and the law, said that no online media could identify the two suspects but that newspapers could and the 6pm television news bulletin could also do so.
The New Zealand Herald said that Harvey had said he was "concerned about someone Googling someone's name and being able to access it later".
The two men are aged 21 and 23 and are to stand trial for the murder of a 14 year old boy, the NZ Herald said. They will appear later this week in Manukau District court.
Judge Harvey said that online outlets could not publish pictures of the two men or name them for fear that people would be able to conduct research on them when the case comes to trial. He said he was "concerned about the viral effect of digital publication".
Research conducted online by jurors in trials is becoming a growing problem for courts. Last week a Newcastle court discharged a manslaughter trial after it emerged that one of the jurors had conducted his own research and had talked to his fellow jurors about the results of it.
Dale Patterson, an 18 year-old, was being tried for the manslaughter of taxi driver Raymond Quigley. One of the jurors visited the crime scene, took his own photographs and looked at the area on Google Maps before discussing his findings with the rest of the jury.
They requested that specific evidence be gathered and gave the judge a list of 37 questions to which they wanted the answers. The judge abandoned the trial.
Earlier this year a case involving child cruelty involving a celebrity nanny at the Old Bailey was also abandoned because it became clear that a juror had down their own research.
When that juror found false information about previous convictions of the defendant and passed it on to other jurors the trial had to be abandoned.
Juries are instructed to base their judgments only on what they hear in the court room during the trial. They are not permitted to use externally-gathered information as the basis for a decision.
