On Sunday, the Dagens Nyheter (DN) daily published an interview with one of the alleged victims, who claims the Church kept quiet on her case for the past two decades despite repeated attempts to obtain justice.
"As a bishop I take full responsibility for that and am prepared to face the consequences," Anders Arborelius, the bishop of Stockholm, Sweden's only Catholic diocese, said in a statement.
He called for "a thorough investigation of this tragic case."
The woman, now in her 60s, told DN she contacted the previous Stockholm bishop, Hubertus Brandenburg, in 1990 to report claims of abuse she and her sister suffered in the late 1950s and 1960s.
"The answer I got was in essence 'We'll do our own investigation within the Church, and it's not something we will talk about'," the woman, who was not identified, told DN.
DN reported that the woman later contacted a Catholic newspaper, which did not take her allegations seriously.
Brandenburg died in 2009, according to the Stockholm diocese.
In 2003, the woman says she met with his successor Anders Arborelius to confront him about the abuse, allegedly committed by a priest who she claims had a sexual relationship with her mother.
When no action was taken, she emailed the Church detailing the allegations, to which she got a reply referring her to a therapist.
She then contacted a high-ranking official in Sweden's Catholic Church to no avail, DN said.
It was only this month, after the Swedish Catholic Church admitted that it had received reports of two other cases of clerical abuse, that the woman's allegations were finally heard out.
She was granted a meeting last week with Bishop Arborelius, who has ordered an investigation.
The woman told DN the bishop was understanding and meant well.
"But I didn't get an answer as to why they only started talking about this now," she said.
The Stockholm Diocese said in Sunday's statement it would not comment further on the case, since the Church was now investigating the matter.
The diocese said the priest accused in the allegations was still alive but no longer lived in Sweden, and that he had not been employed in the Swedish Catholic Church since the mid-1990s.
The Roman Catholic Church is reeling from a string of damning revelations concerning child sexual abuse by Catholic priests in Ireland, Austria, Belgium, the United States and Pope Benedict XVI's native Germany.SIC: INQ