Australia has recently ramped up the deportation of New Zealanders under its tough new stance on non-Australian citizen offenders.
The new stance sees those who aren't citizens and sentenced to a year or more in jail detained and deported.
The man arrested today was not believed to have been deported from the Christmas Island detention centre, 3 News reported.
The nature of his offending in Australia was also not known.
The man was arrested after allegedly going inside a home and fleeing when the burglar alarm went off, 3 News reported.
He was tracked down by dog handlers and no one was injured during the ordeal.
Hamilton deputy mayor Gordon Chesterman said it was "shocking" and "disappointing".
"This is an example of dumping people with issues into an unsuspecting community. I don't think we knew that deportees were coming to Hamilton, so we don't know how many are back and if so shouldn't there be some sort of programme to re-establish them back in the community?"
The man appeared in Hamilton District Court today.
In response to considerable pressure to deal with a substantial increase in the number of Kiwis being deported to New Zealand, the government approved a new "parole-like" monitoring system for overseas offenders deported here.
The Returning Offenders (Management and Information) Bill, went through Parliament using urgency on November 18.
At the time, Justice Minister Amy Adams said the new monitoring regime would cost police and Corrections about $7 million over five years.
It is understood the man was deported before the law change took effect.
Labour leader Andrew Little said he was not surprised at the report given those who arrived back before the law change could not be monitored.
He said he did not know the facts of the case, but many of those being deported had lived in Australia for a long time.
"If you deport someone against their will away from where they've grown up and have family, the risk of re-offending is higher."
Mr Little had just returned from a trip to Australia which included a visit to Villawood Detention Centre.
Labour's Corrections spokesman Kelvin Davis said the blame was at Prime Minister John Key's door.
"It's to be expected. John Key has invited them back and they really want to be in Australia with their families and support networks.
"John Key is just setting New Zealanders up to be victims because these people haven't got the support networks they need."
He said Mr Key should have done more to keep the offenders in Australia.
"I'm not surprised whatsoever that this has occurred."
Australian Prime Minister Malcolm Turnbull and Mr Key had agreed those appealing against deportation orders could return to New Zealand to wait for the appeal rather than go to detention centres.
Mr Davis had visited detainees at Christmas Island and met with one of those who had returned on a flight last week.
Eleven more deportees arrived in New Zealand yesterday, and more were expected to return on commercial flights over the coming week.
Police yesterday said all would be met by police and Corrections staff and undergo the process required under the new act.
Those arriving would also be supported by Prisoners Aid and Rehabilitation Society and other agencies in the coming weeks.
New Zealanders were blamed earlier this month for sparking a riot at the Christmas Island detention centre, which caused millions of dollars of damage.
About 167 had already been deported by then.
The issue sparked acrimony in Parliament after Mr Key accused Labour of supporting rapists and murderers through its advocacy of the Christmas Island detainees - comments he has refused to resile from despite Labour taking offence.
About 585 people were awaiting deportation after the change in Australia's policy to deport all those convicted to more than 12 months in jail.