A Church spokesman said it was "dismayed and ashamed" by the findings.
The report is the latest in a long series of revelations that have uncovered decades of sex abuse by Roman Catholic priests around the world.
Every sixth case involved a rape, and in 75 percent of the cases, the victim and perpetrator knew each other through the church. Most of the victims were boys.
According to the study, 1,670 clergymen in Germany committed some form of sexual attack against 3,677 minors between 1946 and 2014, Spiegel Online reported.
The study was carried out by a team of investigators from three German universities-Mannheim, Heidelberg, and Gießen-under the auspices of the German Bishops' Conference. Again, I emphasize: "The study is a measure that we owe not only to the Church, but above all, and first and foremost, to those affected".
Predator priests were often transferred to another location, but information on their criminal history were not provided to the new site.
Closer to home, Boston Cardinal Sean O'Malley has been implicated - along with Pope Francis - by an archbishop who accuses church leaders of covering up for ex-Cardinal Theodore McCarrick of Washington when he was accused of sexually abusing both children and adults.
Only one in three (566 out of 1,670 accused) were subject to disciplinary hearings by the Church, and most got away with minimal punishment, said Die Zeit weekly, also citing the report.
Asked about the report, a spokesman for the Bishops' Conference told Reuters: "We are checking the matter". He said the Church had planned to provide counselling helplines for people affected by its contents.
The crisis has severely tarnished the standing of Pope Francis and appears likely to undermine it further.
Francis will meet the presidents of the Catholic bishops conferences from around the world in the Vatican from February 21-24, according to a Vatican statement on Wednesday.
Wuerl has faced calls to resign, including from a local deacon at St. Matthew's Cathedral and many other D.C. -area Catholics over his handling of sex abuse allegations by Catholic clergy in Pennsylvania when Wuerl was bishop there almost 30 years ago.
Earlier this week, the Vatican said it is preparing the "necessary clarifications" about accusations that top Vatican officials including Pope Francis covered up the sexual misconduct of a now-disgraced American ex-cardinal.