"It is impertinent and an insult to the victims of sexual abuse as well as victims of the Holocaust," the council's secretary general, Stephan Kramer, said.
The parallel was made in a Good Friday service by Father Raniero Cantalamessa, the pope's personal preacher, who said he received a letter from a Jewish friend criticising the attacks against the pope and Catholic Church over the response to predator priests.
"The stereotyping, the transfer of personal responsibility and blame to a collective blame, reminds me of the most shameful aspects of anti-Semitism," the friend wrote, according to Cantalamessa.
The remarks have triggered a chorus of criticism from Jewish groups and those representing victims of abuse by Catholic priests.
The Vatican "is falling back upon the regular methods it has used over the decades to suppress and hide any affairs which compromise" the Catholic Church, said Kramer.
Vatican spokesman Federico Lombardi later said the comments were from "a letter read by the preacher and not the official position of the Vatican."
But Kramer said he finds it highly unlikely the pope's preacher would make such a statement without Vatican approval.
"It was a step taken at a high level to relativise anti-Semitism and the Holocaust," he said, adding that such remarks make religious dialogue between Jews and Catholics impossible.
The Central Council of Jews in Germany has also criticised a German bishop for comparing the criticism by the press of the Church over the predator priest scandal to Nazi methods.