Small Heath School was inspected by Ofsted following claims it was involved in a take over by hard line Muslims but was found to be "outstanding".
It has since been put into special measures.
Unions say there are plans to convert it to an academy but the council said it was not aware of such a proposal.
Three teaching unions - the National Union of Teachers, the NASUWT and the ATL - are involved in the strike at the secondary school.
The unions said the strike was taking place with "a great deal of regret" after the school's board "failed to give assurances academisation would not take place before the end of autumn term 2015".
David Room, the general secretary of the NUT in Birmingham, said: "We have been forced into this position because we have seen a letter from a senior figure in the local authority saying this school will become an academy."
Ofsted ranked the school "outstanding" in April 2014 under its previous long-serving head teacher, Peter Slough but said it lacked "vision" in inspections in January, following his retirement.
Birmingham City Council said they were "extremely disappointed" by the strike.
It said: "The reason for the strike has been given as potential academisation of the school.
"The Department for Education (DfE) has not approached the city council or the school so far about this."
"If they do, the [board] will ensure that there is immediate consultation with teachers and parents."
The DfE said: "Making sure every child has the chance to get an excellent education and the best start in life is a key priority.
"Ofsted's report on Small Heath School clearly shows that is not happening at the moment."
Staff at a Birmingham school investigated over the Trojan Horse allegations, are striking over fears it could be turned into an academy.