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."

The city council will contribute £4.4m while £12.6m will come from the FA, Premier League and Sport England.
Four "hubs" will be formed on current pitches to reduce a reliance on council subsidies, an authority spokesman said.
The FA has said it will invest a record £260m into grassroots football by 2019.
The leader of the Liverpool council's Liberal Democrat opposition Richard Kemp, however, has warned the deal could cause "major problems".
He said local residents had not been consulted by the FA and Liverpool City Council, and "practicalities had not been worked through" including the presence of floodlights near local residences.
He also questioned whether the council should be contributing funds when it was struggling to maintain parks due to funding cuts, and when the FA was "one of the richest sports organisations in the world".
A council spokesman said members of the public would be consulted after planning applications would be submitted in the "next few months".
City mayor Joe Anderson said it was a "real coup" for the city as the council had "far less money than we used to".
Where will the grassroots football hubs be?
The sites in the first phase of the programme include:
A city council spokesman said discussions were being held with Merseyside Youth Association, who have run three of the sites for nearly 100 years, to restructure their leases.
FA chief executive, Martin Glenn, said the FA aimed to set up football hubs in 30 cities in the next four years to support its youth development.
Sheffield was chosen for the country's first FA-funded grassroots football "hubs" in 2014, when a £9.6m fund was pledged.

A report on 38 North, a website run by the US-Korea Institute at the Johns Hopkins School of Advanced International Studies, studied images taken between April and November.
These appeared to show work in a new area of the Punggye-ri nuclear zone.
But, the report said, there is no sign that any nuclear test is imminent,
North Korea carried out three underground nuclear tests at Punggye-ri in 2006, 2009 and 2013.  Its nuclear programme has been a source of great concern for the international community.
The tunnel identified in the latest imagery is in a new area of the site, separate from three other tunnels that the North has excavated or used for tests in the past, the report said.
"While there are no indications that a nuclear test is imminent, the new tunnel adds to North Korea's ability to conduct additional detonations over the coming years if it chooses to do so," it added.
The commercially-available satellite imagery on which the researchers based their conclusions appear to show a new tunnel entrance, the site's fourth, as well as signs of construction work taking place as recently as October and November.
The report says some analysts believe each entrance connects to a single tunnel but there is debate about the exact nature and structure of the underground testing facility.
It is not the first indication of construction activity at the site.  In October, South Korea's Yonhap news agency quoted a South Korean government source saying there were workers constructing a new tunnel at Punggye-ri.
In September North Korea said that its reactor at the Yongbyon nuclear facility, the source of plutonium for North Korea's nuclear weapons, had resumed normal operations.
Yongbyon's reactor was shut down in 2007 but Pyongyang vowed to restart it in 2013, following its third nuclear test and amid high regional tensions.
Teachers in Powys are set to go on strike on Thursday in protest over "excessive workload and cuts".
[NEXT_CONCEPT]
Liverpool has been chosen as the recipient of the biggest investment into grassroots football after a £17m deal has been agreed.
[NEXT_CONCEPT]
Recent satellite images indicate that North Korea is building a new tunnel at its nuclear test site, a respected US think tank has said.