The National Union of Teachers and National Association of Teachers in Wales will be inviting all teachers at the annual Welsh language and arts festival to sign a petition to be handed over to the Welsh Assembly.
Their dissatisfaction follows restructuring at Estyn, in which four inspectors were replaced by two divisional heads and a post for policy, planning and corporate services was created.
Three of the outgoing staff, who resigned following the reshuffle, were Welsh-speakers. However, Susan Lewis - who replaced Roy James as chief inspector three years ago - doesn't speak Welsh.
The unions will also be protesting at what they see as Estyn's lack of accountability.
Heledd Hayes, education officer for the NUT in Wales, said: "We find it very worrying that there is not one Welsh speaker among the new senior management team. In a country that is bilingual this will create massive problems and seems to demonstrate a total lack of commitment to the Welsh language.
"Fundamentally, we feel Estyn should be more accountable to the Welsh people through the National Assembly. At the moment all appointments are approved by the Queen instead.
"They are basically trying to take us closer to the Office for Standards in Education regime."
Estyn denies that that it will be prevented from functioning effectively and added that the restructuring was approved by the Welsh Language Board.
A spokesperson for Estyn said: "The changes were carried out on the recommendation of an independent management review, in accordance with civil service procedure, and have been approved by the National Assembly.
"There are plenty of Welshspeakers in the organisation and the fact that there aren't any at the top level will not stop it carrying out its job properly.
"We are also completely baffled by the claim that we are not accountable to the Welsh Assembly. We are funded by them and this is simply not the case."