The Auckland Council says it tried to help arrange for a gym teacher to continue running lessons in a Ponsonby building, but received no response from her.
A petition and Facebook page have been started to "Save Leys Gym" by the parents of the 60 children who attend Lynne Burroughs' recreation classes for preschoolers and children aged 5 and over.
For more than 40 years, Ms Burroughs has taught classes in the building, which was built next to the Leys Institute Library complex in 1906 from a bequest made by William Mason.
But from March 9 classes will stop after the council told Ms Burroughs to vacate the building so it can be leased to other occupancy.
Auckland Council spokeswoman Angela Jones said although Ms Burroughs had served the community for many years, there had never been a formal lease arrangement, nor had she ever paid rent to the council.