The venture in Oldham, Lancashire, had been heralded as a way of tackling religious segregation and promoting community cohesion.
Sir Cyril Taylor, former chairman of the Specialist Schools and Academies Trust, had hoped it would be the first of several similar academies across the country to help counter Muslim extremism.
Oldham was the scene of race riots in 2001 after tensions grew between sections of the white and south Asian communities. The Ritchie report into the riots said there were few opportunities for young people to mix across communal boundaries.
But the local council has dropped the joint bid for an academy by the Church of England and Peacemaker, a Muslim-led charity. Having initially supported the partnership, the authority decided it had enough faith schools.
The council will instead seek sponsorship from a further or higher education establishment, which are now exempt from paying any contribution to academies.
Raja Miah, chief executive of Peacemaker, said he was very disappointed by the decision.
"Faith is increasingly dominant in young Muslims' identity and we need to make sure it is represented in mainstream education," he said. "If we don't, we fear an expansion of exclusive Muslim-based schools, and that will add to segregation."
A report published by Lancaster University this week, concluded that mono-cultural white or Asian schools should be avoided. The study, based on interviews with 400 pupils in the North East, said such schools could damage community relations, perpetuate extremist attitudes among white people and fail to prepare young Asian Muslims for prejudice they may encounter later.
Oldham is building three new academies to replace schools which will means redrawing catchment areas. This is likely to lead to more ethnically diverse schools.
The sponsor replacing the Church of England and Peacemaker will be encouraged to invite both organisations on to its board of governors. But the school will not be a designated faith school. Edutrust, a multi-faith charity led by the Muslim peer Lord Bhatia, is expected to sponsor one of the other academies.
Maurice Smith, the director of education in the Diocese of Manchester, said: "In Oldham there have been inter-faith difficulties and we felt this project had something to contribute. We look forward to working with Peacemaker and the council in a different way."
Ed Balls, the Schools Secretary, has said he is not encouraging increased faith school numbers. But a document published by ministers last year, appeared to pave the way for an expansion in faith-based provision, including moving independent Muslim schools into the state system.