Mary McAleese said her brother only revealed the abuse at the age of 49.
She said the physical abuse happened throughout his seven years at St Colman's College in Newry, where Finnegan - who died in 2002 - taught for 20 years.
Mrs McAleese said: "My baby brother, the youngest of nine children was seriously, physically, sadistically abused by Malachy Finnegan."
She said her mother only found out three weeks ago.
Four of the former president's five brothers attended St Colman's.
She choked back tears as she talked about the impact on her family.
"My wonderful, beautiful and as you can imagine the youngest of the family so incredibly loved by all of us, to think that he suffered and never felt that he could tell anyone," she told RTE.
Opportunities to take action were missed, she said.
Mrs McAleese added: "It was known and as he pointed out so many people had to have known, so many people who could have done something about it.
"We know the very first complaints about Malachy Finnegan go back to the 1970s, not the 1990s at all which means there is a body of information known to people who could have done something about it but, didn't."
Finnegan, who taught at St Colman's from 1967 to 1976 has been linked to a catalogue of physical and emotional abuse against pupils.
Earlier this month Bishop of Dromore John McAreavey resigned after it emerged he had decided to celebrate Mass with Finnegan in 2002, despite being aware of his past.
Meanwhile, Amnesty International has repeated calls for a public inquiry into clerical child abuse.
Patrick Corrigan, Amnesty International's Northern Ireland Programme Director, said: "We extend our solidarity to Mrs McAleese's family at this time of great pain for them and many other families, coming to grips with the knowledge that loved ones were left to suffer grievously.
"Sadly, the Father Finnegan abuse scandal is not an isolated case. It is the latest example of how paedophile priests appear to have been facilitated by the Catholic Church authorities in continuing their criminal behaviour.
"Amnesty has written to the Secretary of State to ask her establish a public inquiry into the state and church response to clerical child abuse in Northern Ireland.
"The Irish government established three separate inquiries into clerical child abuse. In Northern Ireland, there has been no similar inquiry and it now falls to the Secretary of State to put that right."
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