An Auckland court granted the man interim name suppression this month but Google revealed his identity in an email to subscribers of its "what's trending in New Zealand?" service.
Justice Minister Andrew Little said the breach was unacceptable and he had made his views known to Google executives at a meeting in parliament on Tuesday night.
While Google has argued the breach was inadvertent and it was unaware of the court order when the automatically generated email went out, Little said that was not good enough.
"I put the ball back in their court," he told commercial radio on Wednesday.
"If they choose to set up their algorithms and distribute news, they've got to take responsibility for that."
The case concerns the murder of British tourist Grace Millane, 22, whose body was found earlier this month just outside Auckland, resulting in a 26-year-old man being arrested and charged.
The case generated intense interest in New Zealand and Britain, where some media outlets have also named the accused, arguing the court order does not apply to them.
Little said he met two local Google executives, and a senior legal counsel from the company's California headquarters joined them by video.
He said they appeared genuinely concerned about the breach and assured him they were working to ensure it did not happen again, with another meeting scheduled for early 2019 to assess their progress.
Little conceded that controlling information on the internet and social media was challenging but said court orders were made for a reason and must be respected.
"We can't just stand back and say this is all too hard," he said.
"The price of that (would be) we have to capitulate and concede what are very important rights that anyone going through the courts has."
He said the case highlighted the potential need for an international agreement if Google "won't do anything (or) can't do anything" to resolve the issue.
"They can expect us to talk to partner countries around the world who have a similar interest... about reaching an agreement to enforce each others' orders in each others' countries," he said.
"That may well happen inevitably anyway because it's not just Google, there are others as well and we have to protect the integrity of our court system."