Father Francis Davidson has been accused of failing to act on reports during his time at the Catholic Fort Augustus Abbey School in the Highlands in the 1970s.
He has quit as monastic superior of the Benedictine college St Benet's Hall, where he was responsible for the welfare of student monks at the university.
Alleged victims who attended the Abbey school told a BBC Scotland investigation that they were molested and beaten by monks over a period of three decades from the 1950s.
It has also been claimed that abuse was carried out at Carlekemp, its feeder school in East Lothian. Both schools are now closed.
Police are investigating the allegations.
One former pupil said that he told Fr Davidson personally of the abuse but the monks remained in the Abbey. Fr Davidson is the only surviving headmaster of the school.
In a statement, Fr Davidson offered his sympathies to former pupils for any historic abuse and said he was "shocked and saddened" to hear of the allegations.
He added: "I do not recall them being reported to me during my time as headmaster of Fort Augustus Abbey School.
"As investigations into matters at Fort Augustus Abbey School and Carlekemp Priory School are ongoing, I have stepped aside from my role as religious superior at St. Benet's Hall."
Earlier this month, one of Scotland's most senior Catholics apologised to former pupils amid the claims.
Hugh Gilbert, the Bishop of Aberdeen, said: "It is a most bitter, shaming and distressing thing that in this former Abbey School a small number of baptised, consecrated and ordained Christian men physically or sexually abused those in their care."
Anne Houston, chief executive of charity Children 1st, said: "The focus here must always remain on what's best for those who were abused in the past and what will make a positive difference to them; that and helping protect children now and in future by taking steps to minimise the risk of this ever happening again.
"It is crucial that the church fully and openly co-operates with the ongoing police investigation and passes on any and all relevant information it may have relating to any allegations of abuse at these schools."