The report released on Tuesday concludes at least 3,677 people were abused by clergy between 1946 and 2014.
"Sexual abuse is a crime," Cardinal Reinhard Marx, who is also the head of the German Bishops Conference, told reporters.
"I'm ashamed for so many (of us) looking away, not wanting to recognise what happened and not helping the victims. That goes for me as well."
The apology came on the day Pope Francis acknowledged the sex abuse scandal rocking the Catholic Church was driving people away. He said the church must change its ways if it wants to keep future generations.
The report on sex abuse in the German Catholic Church found that more than half of the victims were 13 or younger and most were boys.
Every sixth case involved rape and at least 1,670 clergy were involved. Some 969 abuse victims were altar boys.
On average, the abuses happened multiple times over a period of at least 15 months.
The German Bishops Conference released its report on Tuesday, but it had already been leaked earlier this month and was heavily criticised for the lack of transparency and the church's refusal to let the researchers access original documents.
Instead of looking at the original church files, they sent questionnaires to the dioceses, which then provided the information.
The report was commissioned by the German Bishops Conference and researched by experts from the universities of Giessen, Heidelberg and Mannheim.
The researchers wrote that there was evidence that some files were manipulated or destroyed, and many cases were not brought to justice.
Sometimes abuse suspects - primarily priests - were simply moved to other dioceses without the congregations being informed about their past.
"The figures are only the tip of the iceberg," said Harald Dressing, a psychiatrist from Mannheim University who presented the report with Mr Marx and others in the central German city of Fulda during a convention of the German Bishops Conference.
"Generally, the risk of sexual abuse of children inside the Catholic Church continues to exist," Mr Dressing warned. He said celibacy, the clergy's power and homosexuality inside the church were all issues that promoted abuse.
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