Infections from the novel coronavirus spread to more than 8100 people globally and has claimed 171 lives.
The Ministry of Education advised schools on Monday to ask any students coming from China to stay away from school for two weeks.
A student liaison with the New Zealand Institute of International Education, Charm Money, said some homestays had asked students to find other accommodation over that period.
She said the students were either staying with friends or in other rented accommodation.
Some students in China are also delaying their travel to New Zealand after schools here advised them to wait for two weeks.
Auckland's Elim Christian College principal Murray Burton said some students and staff had been asked to stay away from school for a fortnight.
"We've got upwards of 30 students ... local students who will not be returning on Monday because they need to wait for two weeks. We've got five staff who will not be returning on Monday.
"They're very cooperative and we'll work our way through that."
National Party's education spokesperson Nikki Kaye told Morning Report she's also hearing about students stuck in a cycle of being rejected.
"You may have students who may have test results and they've been to Hubei province, being requested to go back in with those accommodation providers and then [being refused].
"I'm being briefed by the Ministry of Education today and so I have a range of other questions about their response and contingency planning."
She said she believed that risk to other students could be mitigated through alternative accommodation or isolation beds.
"There's a huge difference between a student from Hubei province that is displaying symptoms, has got test results potentially coming back, and then a family that may have rejected a homestay student because they're scared or they may have young children."
Kaye said she was referring any situation she was aware of directly to ministers.
But she said the broader problem was that each institution had a different capacity in dealing with the situation, and some required more support.
Advice to homestay families and schools
Director-General of Health Dr Ashley Bloomfield said the Ministry of Education had information on its website for families who host homestay students.
"The key thing is the schools at which the students are registered are under an obligation to work with homestay families and/or if they need to provide temporary accommodation for students, to work with the students."
The Ministry of Education on its website has advised schools and families that international students should continue to feel welcome.
"We want to reassure homestay carers that if a student is staying home, it is a precautionary measure [to stay away from school for two weeks], and that the student does not need to supervised if they are not ill and over 14."
It said if there were concerns about hosting students who may have been exposed to the virus then the affiliated school should be contacted.
"If a student does not shows signs of illness after 14 days, then they should return to school and continue their studies as normal."
It said that carers already looked after international students as per the contract between homestay families and schools.
"Should homestay carers be unwilling to take a student who has returned from China until after the stay home period the school will need to find a short-term solution until the 14 days has ended."
If homestay carers or students have concerns, they should contact Healthline on 0800 611 116, or the GP for medical advice.
Healthline has translators and interpreters available 24/7 in 150 languages, and Mandarin and Cantonese speaking staff are available.
Accommodation provider screening arrivals
John Chen, who owns the Empire, Columbia, and Princeton Student Accommodations in Auckland, said he had taken two students with temperatures to hospital, rather than leave them in their accommodation.
One of them was now in isolation, he said.
However, Health Minister David Clark yesterday said there had not been any suspected cases in New Zealand and that the public and media should treat rumours of any cases in this country "with some caution".
"If and when we get a case, we will be telling the public promptly. We have not yet had a case of coronavirus. So far we have not had anyone who has met the definition of a suspected case."
Chen told RNZ's Lately that they screened all the existing students as well as arriving, and ones with symptoms were sent to Auckland Hospital.
"We have a questionnaire they fill out... [ask them about] flu symptoms, and coughing, fever, etc, and we also measure their temperature ... and then the consequence is that my staff deals with it, if they suspect a case they send them to the hospital."
He said the other student was released from hospital, but their rooms were full when she came back at night.
"We didn't have any room, and then we made arrangements for her to move to another accommodation."
He said he only housed students at tertiary level and has about 1200, but there were some arriving in the country as young as 10 years old.
"I mean they're scared enough as it is coming on the plane here, I don't think they were thinking of coming to a situation like this."
He said he felt he was somehow expected to take responsibility for the students' welfare and ensure they went to a doctor or isolate them if need be.
Chen said he's been in touch with Nikki Kaye and the public health department, but could not provide isolation for students because they were not equipped for it.
"We have hospitality trained staff but not medically trained staff... but I would not agree to something like that because there's a high chance that my staff will be infected if they go in and out of these rooms."
He said he's keeping in touch with the isolated student and the one that had to be turned back because he was concerned for them.