The Right Reverend Cuthbert Madden, chairman of governors and abbot at Ampleforth College, has denied any wrongdoing.
He has been at the Benedictine monk-run college for more than 30 years and was elected abbot in 2005.
A police spokesman said: “North Yorkshire Police is investigating non-recent allegations of indecent assault against four pupils at Ampleforth College which took place in the 1990s.
“The information was reported to the police in August 2016. The investigation remains ongoing and a man in his 60s has been interviewed under caution.
“The police investigation has also triggered safeguarding measures which have been put in place while the investigation continues.”
The school has a history of allegations of abuse with a number of previous convictions, including Father Piers Grant-Ferris who was jailed for two years in 2006 for 20 counts of indecent assault on boys in his care.
The force also confirmed they were “conducting two other inquiries into alleged sexual abuse at the college”.
The school, which opened in 1802 as a boys’ school, has over 600 pupils and admitted girls for the first time in 2002. Some of its famous former pupils include Downton Abbey creator Julian Fellowes and former England rugby captain Lawrence Dallaglio.
A statement on the abbey’s website said: “Following allegations relating to historical events, Abbot Cuthbert Madden has temporarily stepped aside from his responsibilities as Abbot of Ampleforth.
“Abbot Cuthbert denies any wrongdoing and will be co-operating fully whilst the allegations are investigated by the appropriate authorities.
“In the interests of transparency, we want to ensure the Ampleforth community and friends are aware of the current situation.
“This course of action accords fully with established civil and ecclesiastical protocols, and is a neutral action, which will remain in place for the duration of the investigation.
“Father Terence Richardson, the Prior of Ampleforth Abbey, has full delegated authority to act as the Religious Superior of Ampleforth Abbey during this time.”
A letter was also sent to parents from the headmaster, Father Wulstan Peterburs, to let them know about the investigation into Abbot Cuthbert.
It said: “I write at the earliest opportunity to inform you that, following the receipt of allegations relating to historical events, Abbot Cuthbert Madden has temporarily stepped aside from his responsibilities as Abbot.
“This course of action accords fully with both established civil and ecclesiastical protocols and implies neither guilt nor innocence; it is rather a neutral action that will remain in force whilst the allegations are investigated by the appropriate authorities and due process is allowed to continue unimpeded. Abbot Cuthbert denies all wrongdoing.”
“Father Terence Richardson, the Prior of Ampleforth Abbey, has full devolved authority to act as the Religious Superior of Ampleforth Abbey. The Chair of the St Laurence Education Trust (responsible for Ampleforth College and St Martin’s Ampleforth) will be temporarily taken by the Vice-Chair, Mr James O’Neill.”
It issued a statement in relation to the case of Paul Sheppard, a former teacher who was last year acquitted of indecently assaulting a pupil.
The force said it had carried out a “complex investigation” into allegations made against Dr Sheppard and made “considerable efforts to present a strong case on a number of allegations” to prosecutors.
This case is the subject of a review by senior officers at North Yorkshire Police as part of the ongoing Independent Inquiry into Child Sexual Abuse.
The Yorkshire Post revealed in 2005 that pupils suffered decades of abuse from at least six paedophiles following a decision by former Abbot Basil Hume not to call in police at the beginning of the scandal, which was not linked to Dr Sheppard.
The school now employs a specialist ex-police officer as a safeguarding co-ordinator who works closely with its independent safeguarding commission.