Associate Minister of Health Peeni Henare said there had also been problems at managed isolation and quarantine facility Jet Park involving gangs and police were now investigating allegations rooms had been trashed.
"I can confirm there has been a challenge there and troubles there. There has been a bit of vandalism, the extent of that I'm not completely sure," Henare told the AM Show today.
"This is obviously a disruption in our quarantine facility space and I know that the police have been engaged so that we can continue to keep the community safe while also stopping this kind of behaviour. It's just not acceptable."
"My expectation is whoever does that kind of vandalism in a place like that should be charged with the expenses and hopefully that's what happens. It's certainly something I'll be advocating for."
Hamilton's index case has known connections to Kawhia and Raglan.
A post on a community Facebook page alleged the person breached the Auckland boundary, apparently to purchase drugs. They collected a "supply" of some substance, which was taken to the Waikato.
The post said the man, who is currently in hospital, had "been supplying to the communities of Raglan and Kawhia for many years", and urged people who had been in contact with him to destroy their supply and get a test.
The post suggests the man breached the Auckland boundary to pick up a supply of some substance, which was then delivered to people in the community.
It warns that the "bags" of supply are possibly contaminated with Covid-19, despite little evidence the virus can survive on surfaces. The poster says people need not hand over the bags to police, but they should destroy the bags and get a Covid-19 test.
"[A]fter preaching [breaching] the Auckland borders to pick up his supply we must presume that the bags are contaminated,"
"I'm not asking you to give the contents of the bag's [sic] over to the police but the bags need to be destroyed and you need to get a Covid-19 test this is what you need to do to keep the Kawhia Community healthy and safe"
The post, which was later removed, appears to have energised members of the group who warned that unmasking the patient could have negative consequences on their family.
The person is currently on e-bail in Hamilton and had not visited Kawhia while infectious.
"Please be mindful of those that maybe [sic] affected by what you would deem a service to the community by naming and shaming a person because of the choices, weather [sic] negative or positive, make.
"Think of those that aren't involved in certain undesirable activities, those that lead an honest law-abiding life and the negative attention to them that naming and shaming can bring,"
The Government acknowledged on Wednesday that "quite a number" of people in the latest outbreak were gang members.
Covid-19 Response Minister Chris Hipkins noted that some people in the outbreak had been more "active" than permissible under alert levels.
David Bennett, the local National MP, said the criminal connections of the Hamilton cases should have been disclosed to residents.
"It's been extremely disappointing the Government has taken this approach to the residents of Hamilton," Bennett said.
"They haven't been upfront with the people concerned and their gang affiliations," he said.
"They've treated the people of Hamilton like fools."