Hundreds of seasonal workers have been stranded in New Zealand over recent months, some with expiring visas.
Pacific leaders had already raised concern about those with uncertain immigration status missing out on assistance or healthcare because of fear of being discovered.
However the minister, Chris Hipkins, encouraged them to get tested for Covid-19 if they needed to.
"We will not use the information collected through the Covid-19 testing process for other purposes, including for immigration purposes," Mr Hipkins said.
"We do not want people not to be getting a test for fear of the repercussions because of their immigration status.
"What is most important now is the public health response so go and get a test. We won't use the information they supply for that testing process for immigration purposes."