A Vatican statement said the Pope accepted the resignation of Bishop Donal Murray following the report, which said Church leaders in overwhelmingly Catholic Ireland had covered up widespread sexual abuse of children by priests for 30 years, Reuters reported.
Murray, the first Irish bishop to quit since the report's publication last month, was criticized for his handling of complaints about abuse in the diocese of Dublin.
"I humbly apologize once again to all those who were abused as little children," he told churchgoers attending mass in St John's Cathedral in Limerick.
He added that his resignation "cannot undo the pain" of abuse survivors.
Church sources have said a number of bishops mentioned by the report are likely to offer to resign, in what they said would lead to a shake-up of the Irish Roman Catholic Church.
Murray served for 14 years, until 1996, as auxiliary bishop in the Archdiocese of Dublin before being appointed to the diocese of Limerick.
"I asked the Holy Father to allow me to resign and to appoint a new bishop to the Diocese because I believe that my presence will create difficulties for some of the survivors who must have first place in our thoughts and prayers," Murray said.
The Vatican statement did not mention the scandal but said Pope Benedict had accepted Murray's resignation according to a clause of Canon (Church) Law that calls on bishops to quit if they cannot fulfill their duties for a "serious reason."
The Murphy Commission Report came six months after the release of a similarly damning and even more graphic report about floggings, slave labor and gang rape in Ireland's now defunct Church-run industrial and reform schools in the 20th century.
The report issued on November 26 found the Church had "obsessively" hidden child abuse from 1975 to 2004.
The paper said that of the 13 auxiliary (assistant) bishops in the archdiocese who knew about complaints of child sexual abuse over that period, four -- including Murray -- "dealt particularly badly with complaints."
It said the archdiocese had been more preoccupied with protecting the reputation of the church than safeguarding children's welfare.
Murray "did not deal properly" with the suspicions and concerns expressed to him in relation to one priest, Father Tom Naughton, in 1983, the report said.
A short time later, evidence of Naughton's abusing emerged in another parish.
"Bishop Murray's failure to reinvestigate the earlier suspicions was inexcusable," the report said.
Irish church leaders last week met the Pope, who expressed "outrage, betrayal and shame" over the affair.
The church's moral authority in Ireland has been eroded in recent years following a string of clerical sex abuse scandals, many of them involving priests molesting young boys.
Similar abuse cover-up charges have dogged the Catholic Church in other countries, especially the United States. Seven dioceses there have filed for bankruptcy protection to shield themselves from law suits by abuse victims.