Former priest Michael Steve Baker informed Mahony two decades ago of his abusive acts but was allowed to remain in the ministry.
His case has become a symbol of how the church transferred priests who abused young boys.
He is now in U.S. federal custody, said the source, who spoke on the condition of anonymity because the case is ongoing.
The news comes six months after The Times reported that the U.S. attorney in Los Angeles had launched a federal grand jury investigation into the response of the L..A. church into allegations of molestation by priests in the archdiocese.
The probe is aimed at determining whether Mahony, and possibly other church leaders, committed "honest services fraud" by failing to adequately deal with priests accused of sexually abusing children, sources said.
Mahony's attorney has said Mahony is not a target of the federal inquiry, adding the cardinal was fully cooperating with federal officials.
As the Roman Catholic Church's highest-ranking official in Southern California, Mahony was dogged for years by allegations of covering up the sexual misconduct of priests.
Two years ago the archdiocese agreed to pay $660 million to 508 people who accused priests of sexual abuse.
The payout is the largest settlement in a scandal that rocked the Roman Catholic Church nationwide.
Baker in 1986 told Mahony that he had molested children, but he was allowed to remain in active ministry.
Mahony sent Baker to a treatment center in New Mexico and later reassigned him to other parishes, where he allegedly victimized at least one other child.
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