The Ministry of Social Development has been providing benefits to migrants since it took over from a Red Cross support scheme last year.
The founder of migration thinktank The Fair Initiative, Charlotte te Riet Scholten-Phillips, said migrants pay the same taxes and should be allowed benefits because Covid-19 had created extraordinary circumstances.
"It's very disappointing that the government has decided to stop these benefits when there's obviously still a need," she said.
"It's distressing to hear constant reference to the 'team of 5 million' and how our wonderful essential workers are contributing to our Covid response, but when the migrants in that team need help we're cast aside.
"How is it that one moment we're part of the 'team' or 'essential' and the next it's OK to force migrants into poverty and possible homelessness - is this what New Zealand is now? What happened to our fabled kindness?"
Among temporary visa holders are an estimated 25,000 international students, who are limited to working 20 hours a week.
The International Students Association (NZISA) was told by the Ministry of Social Development that emergency benefits were only available to temporary visa holders as a short-term solution while they arranged to return to their home countries or found work.
Advice on the Ministry of Social Development website says those still needing support should contact their embassy.
NZISA is also upset that a hardship fund is only available to domestic New Zealand students, when it was offered to international students during last year's lockdown.
Some were struggling to find work, especially as they were not allowed to work full-time unless they're supermarket staff, said its president Afiqah Ramizi.
"Normally international students would be funded either by the family members, or by scholarship," she said. "The problem with the majority who are funded by their family members is that other countries are in a worse position due to Covid-19.
"International students also have told us that they have not received any responses from their embassies, when they reach out for support at this time.
"It's bad timing that the benefits expire now. We did request for more time, we asked for at least the cover at level 4 and 3."
She said it was a lot to ask of students to return to their home countries - forfeiting the money they had paid for their courses, and the time they had spent on uncompleted studies - and returning to countries where Covid-19 was a very real danger.
"NZISA is extremely disappointed at the government's and education providers' inaction and the lack of support for international students during this time of crisis," Ramizi said.
"We pay extensive international student fees, support local economies, and contribute to the New Zealand job market. At the same time we are cut off from our families who are also struggling abroad.
"This disparity between the support given to international students and domestic students continues to drive a wedge between our communities. It goes to show that international students aren't a valued community.
"Immigration New Zealand could model the Canadian government's approach in removing the 20-hour cap for all international students working in priority sectors over lockdown."
MSD said those migrants receiving an emergency benefit will get their final two days of payment in the week beginning 6 September.
Group general manager of client service delivery Kay Read said people who need further support or repatriation advice should contact their Embassy, High Commission or Consulate.
"MSD's Community Connectors will also be available to help temporary visa holders who are currently receiving an Emergency Benefit to help them engage with foreign missions, and other available community and non-government organisation support," Read said.
"Immigration New Zealand (INZ) is also continuing to provide funding through the INZ Repatriation Fund. This fund assists people who are in hardship and need help with paying for travel to return to their home country."
MSD said any decision to extend the availability of benefits would be for ministers to consider.
In a statement, the Ministry of Education said the $1 million International Student Hardship Fund was set up in May 2020 and it had been distributed to about 4000 students.
"The Hardship Fund for Learners helps tertiary education organisations provide temporary financial assistance to domestic tertiary learners who face hardship due to the Covid-19 pandemic," said the Ministry of Education's group manager tertiary Belinda Himion.
"Since the return to alert level 4, officials have been meeting regularly with peak body organisations, including international student leaders, to understand and respond to the needs of the sector."