Rod Weatherhead, head of Heybrook community primary, has been suspended until further notice, pending an investigation into alleged irregularities in the key stage 2 tests.
Rochdale Council said: "Suspension is a neutral act under the disciplinary procedure and should not be taken to mean that the suspended employee is at fault.
"The matters that have come to light are being thoroughly investigated and we hope to conclude the investigation as son as possible."
All Heybrook's 486 pupils are Muslim. It is alleged that Mr Weatherhead allowed pupils to sit their exams in a local mosque before a trip to Pakistan. Neither the school nor the council would comment on the allegations.
The key stage 2 tests in maths, English and science took place nationally last week.
The Qualifications and Curriculum Authority said tests could only take place outside the scheduled test period in exceptional circumstances. A spokeswoman would not comment on the Heybrook case.
Tina Wheatley, deputy head at Heybrook, is now acting head.