Mark Keary is principal at Green Spring Academy Shoreditch in east London, and is reportedly paid Â£220,000 per year.
He was in charge when three girls from the school - formerly Bethnal Green Academy - fled to join so-called Islamic State in Syria.
Green Spring Education Trust confirmed he was one of "a number" of staff suspended pending an inquiry.
In a statement the trust said: "An investigation into alleged misconduct in relation to some examinations has found irregularities.
"The trustees are taking the matter very seriously and are working with the authorities to address concerns and safeguard students taking exams at the academy this year.
"The trust has taken the decision to suspend a number of staff and, in light of this, additional leadership support is being brought in."
The BBC understands the allegations relate to the academic years of 2015-16 and 2016-17.
The academy is one of the top performing schools in the country.
In its latest results it recorded an 83% A-C pupil pass rate for GCSE English and maths.
It was described by Ofsted inspectors as performing "well above the national average" for its progress score, which reflects the amount of value the school has added to its pupils' learning outcome.
The school made headlines in 2015 when three pupils, Kadiza Sultana, Amira Abase and Shamima Begum, aged 15 and 16 at the time, left the UK during February half term for Syria.
A year later, the family of Kadiza Sultana said she was feared dead after an air strike in Raqqa.
Tower Hamlets Council said as an academy the school was independent of the council, but it had made contact and was offering any support it needed.
A spokesman for the Department for Education said: "There is no place for cheating in our schools and while exam malpractice is extremely rare, it is right that any allegations are thoroughly investigated.
"Following an investigation at Green Spring Academy in Tower Hamlets, exam malpractice has been identified resulting in disciplinary action being taken.
"The Regional Schools Commissioner is working closely with the academy trust to ensure students face as little disruption as possible during this time, and we continue to monitor the situation closely."
One of the most highly paid head teachers in the country has been suspended amid claims of exam fixing.