Graham Hardy, from Kettering, Northamptonshire, who is retired from Birmingham's Calthorpe Academy, was arrested on 6 April.
The school has sent a letter to parents stating the alleged offences do not relate to any current or ex pupils.
West Midlands Police said a 63-year-old man had been released on bail.
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The school's current principal, Richard Chapman, joined Calthorpe Academy in January.
Mr Chapman said: "Graham Hardy retired from the school at the end of last year and no longer has any connection with the Academy.
"However we can reassure parents and members of the public that this investigation does not affect the safety or wellbeing of our pupils or staff, or the running of our school."
West Midlands Police said they were working closely with the school as part of an ongoing investigation.
The former head teacher of a school has been arrested on suspicion of sexually assaulting adults and possession of indecent images of children.