They announced their intentions late Monday just after a federal appeals panel gave the green light for New York City to impose the mandate after days of court wrangling.
The city's Department of Education says the mandate will now go into effect at the end of Friday.
The plaintiffs argue that teachers who are placed on unpaid leave because they have not complied with the order will be irreparably harmed.
"There's 28,00 teachers and DOE employees that are not vaccinated and none of them are conspiracy theorists, none of them are anti-government," said Louis Gelormino, attorney for NYC teachers."Most of them just want to make their own choice."
The teachers' request for emergency injunctive relief from SCOTUS was not likely to occur before Friday, added Gelormino.
On Monday, Oct. 4 2021, 100% of approximately 148,000 educators, custodians, cafeteria workers and other staff in public schools must have at least a first dose of the COVID-19 vaccination.
Refusing to comply would result in suspension and termination.