NASUWT said its members want to be able to provide face-to-face teaching in the new term which begins this week.
Justin McCamphill from the union said the Executive must do all it can to prevent schools from experiencing “significant staffing problems”.
There has been a surge of infections by the omicron variant in NI.
On Thursday, Stormont ministers were told that the omicron variant now accounts for about 90% of cases in Northern Ireland.
“We are calling on the Executive to urgently intervene in schools to make sure they’re safe,” Mr McCamphill told the BBC.
“Over the new year we have seen a big increase in the number of cases with the omicron variant so we’re expecting a big amount of disruption in schools when they return this week.
“Unfortunately, that will mean many classes and year groups will be sent home.”
Before Christmas, some schools had to send individual year groups home for remote learning on specific days due to staff absences and difficulty getting substitute teacher cover.
The NASUWT is urging the Executive to: provide air cleaning units to every school and college; support household close contacts to self-isolate to reduce the risk of transmission within schools; commit to providing schools with more resources in the event that on-site Covid testing is again required; provide improved financial support to schools and colleges for the costs of substitute staff; and suspend all non-business critical activities in schools until at least after the spring term.
Sinn Fein education spokesman Pat Sheehan MLA has called on the education minister to urgently revisit her approach to Covid so schools “can remain open safely in the new year”.
He said: “So far, a lack of appropriate guidance, a lack of adequate safety mitigations, a soft-touch contact tracing policy, and a lack of available substitute teachers have put many of our schools in difficult positions with many resorting to partial closure last term,” he said.
Regarding the omicron variant, he said he would “continue to make the case” to the minister to revisit her approach to Covid in schools “to make our classrooms safer”.
Meanwhile, the Public Health Agency (PHA) has confirmed at least 120 care homes in NI have Covid-19 outbreaks.