Sajid Raza, the founder and head of Kings Science Academy in Bradford, one of the Government's first free schools, was arrested at the school today by police investigating an alleged fraud.
The 41-year-old was later bailed by West Yorkshire Police pending further enquiries.
They are looking into the mismanagement of more than £86,000 of public money at the academy.
Last year an Education Funding Agency investigation found the academy to have "serious failings" in its financial management.
Prime Minister David Cameron toured the academy in 2012 and later praised the academy for its "good work".
Bradford East Lib-Dem MP David Ward told ITV News: "Because this is such an important policy area for the Conservatives, the fear I have is that the normal rules of public accountability are being forgotten and put to one side."
ITV sources close to the education secretary Michael Gove denied there had been any kind of cover-up in relation to Kings Science Academy.
The Department for Education said today that "all free schools are held to rigorous account" and that it acted as soon as it received allegations of wrongdoing at the academy.
– Department for Education spokesman
The department acted as soon as it received allegations of wrongdoing at Kings Science Academy.
We formally investigated and referred the case to Action Fraud. This resulted in a police investigation which is ongoing. Separately we are recovering appropriate funds.
All free schools are held to rigorous account. The vast majority are performing well with three-quarters rated good or outstanding. But where there is failure we will not hesitate to intervene.
Education officials insist that despite the police investigation there's no question of the school itself being in any way at risk.
Watch Libby Wiener's report on the investigation into the school's finances:**