The government has changed immigration rules to help supermarkets cope with labour shortages.
Supermarkets will be able to change the roles and other work conditions of staff who are on work and student visas.
But uncertainty remains for immigrants in other sectors who lose their jobs.
A spokesperson for the immigration minister, Iain Lees-Galloway, said they would be able to access an emergency benefit if they lost their job.
But late today his office said only that that was "something that is being worked on and options have not been decided yet".
And the Ministry of Social Development (MSD) said its only advice to tourists and foreign workers was to talk to their embassy.
The MSD's client service delivery manager George van Ooyen said that included workers here on the Recognised Seasonal Employer scheme, working holiday, short-term visa, students and tourists.
"Covid-19 wage subsidies and leave payments, are available to people on temporary work visas and anyone else legally working in New Zealand," he said.
"We understand the current situation is impacting people in many ways and are doing all we can to provide assistance to people in need."
Queenstown Mayor Jim Boult said the immigration minister had assured him last week hardship grants would be made available, and in the meantime the community had rallied around.
A system of vouchers for food parcels has been arranged for foreign workers, he said.
At the peak of the season the city had 3,000 foreign workers and many have been laid off.
"We set up an online registration system for those who have lost the jobs, have no place to get an income from and are worried about being thrown out of their accommodation and we have 600 registered on that database already," he said.
INZ said in a statement immigrant supermarket workers can temporarily change roles and other visa conditions, and students who are employed in those stores can work work more than their usual 20 hours a week in supermarkets.
"These changes have been made in response to supermarkets experiencing immediate labour supply issues, particularly to meet the increased demand for shelf re-stocking," it said in a written statement.
"These visa measures apply to supermarkets operated by Woolworths New Zealand (owners of Countdown, Super Value and FreshChoice supermarkets) and Foodstuffs Limited (owners of New World, Pak n Save and Four Square).
"INZ is continuing to work with the Ministry of Social Development and other relevant agencies to develop support for migrants as part of the All of Government Covid-19 response."