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.
According to the new study, only 38% of the alleged perpetrators were prosecuted with most facing only minor disciplinary procedures, German media said. About one in six cases involved rape.
Most of the victims were boys, and more than half were aged 13 or younger.
Predatory clerics were often moved to new communities, where no warning was issued about their actions.
The study was compiled by three German universities, using 38,000 documents from 27 German dioceses. Its authors said the true extent of the abuse may be even greater, as some records were "destroyed or manipulated".
How has the Catholic Church reacted?
"We know the extent of the sexual abuse that has been demonstrated by the study. We are dismayed and ashamed by it," said Bishop Stephan Ackermann, a spokesman for the German Bishops' Conference which commissioned the report.
He said the aim of the study was to shed light on "this dark side of our Church, for the sake of those affected, but also for us ourselves to see the errors and to do everything to prevent them from being repeated".
"I stress that the study is a measure that we owe not only to the Church but first and foremost, to those affected," the bishop added.
Pope Francis and Irish PM Leo Varadkar spoke out on the abuse last month
Bishop Ackermann said the report had been leaked to the press before the Church itself had seen it. He said the Church had planned to provide counselling helplines for people affected by its contents.
What is the Church doing about abuse claims?
The Vatican did not immediately respond to Spiegel's account of the report. But elsewhere on Wednesday, Pope Francis summoned Catholic bishops to the Vatican for a discussion on how to protect children in February next year.
The damning German study is the latest in a series of blows to the Roman Catholic Church.
Claims of clerical sex abuse have been levelled around the world, and with them allegations that Church leaders hushed up or ignored the wrongdoing.
Pope Francis was caught up in the scandal last month, after a former Vatican diplomat accused him of ignoring allegations against a US cardinal for five years.
The Pope's supporters vehemently question the credibility of this accusation, which the pontiff has refused to respond to.
It came after a grand jury report detailed seven decades of abuse in the US state of Pennsylvania. The investigation found more than 1,000 children had been abused by 300 priests there. It found evidence of systematic cover-ups by the Church.
"It's your word against God's": The office of the attorney general in Pennsylvania released video testimony from three victims
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