Members of the National Union of Teachers (NUT) said it was to highlight wider problems including teacher redundancies.
Powys council's cabinet member for schools, Arwel Jones, said he was "surprised and disappointed".
The NUT said it represented about half of teachers in Powys and 83.5% of those balloted voted in favour of action.
The council is currently consulting on plans to reorganise secondary schools.
Mr Jones added: "Strike action will not deflect our programme but could disrupt the work of school pupils at a crucial time."
Teachers in Powys are set to go on strike on Thursday in protest over "excessive workload and cuts".