The victim was one of two people asked to sign an oath of confidentiality at two secret canonical inquiries which Brady attended in 1975.
Brady subsequently failed to report the allegations to civil authorities.
The female victim first brought her High Court case in 1997 and has been involved in a legal battle since then in a bid to force disclosure of the documents relating to the handling of her case by the church.
Brady responded to calls on Friday for him to withdraw his defence in a separate legal action taken by a male victim of Smyth by announcing that he had asked his legal representatives to engage with the complainant's legal representative "with a view to progressing the case".
However, asked by this newspaper if, in light of recent revelations and his public pronouncements, he still intended to contest the High Court action by Smyth's female victim, Brady's spokesman said he would "maintain his right to defend himself, both in his personal capacity and as Primate of All-Ireland, while seeking a just resolution for all involved".
The response comes amid reports yesterday that Brady would be forced by the Vatican to quit his post, although these have been dismissed by his spokesman.
Brady's approach to the High Court case has been criticised by abuse survivor Marie Collins, and Maeve Lewis of victims' group One in Four, who noted the detrimental effect which such lengthy cases can have on victims.
"What Cardinal Brady is saying about care for the victims, and then allowing this sort of thing to drag on for years and years, is contradictory," Collins said.
"Given Cardinal Brady's apologies… it is very surprising that he would continue to defend his position," Lewis added.
Meanwhile, it has emerged that Brady has been named a co-defendant, along with the head of Brendan Smyth's Norbertine Order, Gerard Cusack, in a total of five High Court cases since 1997. The latest of these was filed in 2003.
The Sunday Tribune asked Brady's spokesman for details of his involvement in these cases, including how many of them had led to an out-of-court settlement; and whether they included a requirement to sign a confidentiality clause. But he declined to provide this information.
"Regarding your questions, I only know of two cases, both of which are in the public domain. In any event, Cardinal Brady cannot comment on these cases."
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