Peters said Australia had the sovereign right to decide on domestic issues, but both New Zealand and Australia were signatories to that convention.
"This person is a child, or a minor and I'm just reminding the Australians 'you're a signatory, live up to it.'
"They are clearly in breach of it. There's no complication. They know that, we know that."
Peters said the Government had already made its displeasure about that case, and the wider deportation policy, clear to the Australian Government.
He would see Australia's Foreign Minister Julie Bishop in Australia in August and would again voice his concern.
"The Australians are very aware of what our views are on that and the expulsion of so many New Zealanders from Australia, some of whom have only been in New Zealand for their total lives for three or four years."
Australia also introduced a new hardline policy in December 2014, allowing the deportation of non-Australian citizens who have served sentences of more than 12 months back to their homelands.
There are also provisions for deportation on character grounds, if somebody is deemed a danger to the community.
Both the National and Labour governments have tried to get Australia to drop or soften the policy when it comes to New Zealanders but it has refused to do so.
The deportations were initially restricted to over 18-year-olds.
The only concession gained was for the length of time a potential deportee had lived in Australia to be taken into account when appeals against deportations were held.
Labour had raised issues with the policy when in Opposition, including sending its corrections spokesman Kelvin Davis to speak to New Zealanders detained at Christmas Island.
Davis is now Corrections Minister but said he did not know much about the case and other ministers, including Foreign Minister Winston Peters, were dealing with the detention issue.
"I still hold very strong views about it, but there are ministers responsible for addressing these issues at the appropriate level."
More than 1000 people have been deported back to New Zealand under the 2014 policy, prompting New Zealand authorities to set up a special strategy and monitoring to try to prevent re-offending.