The poll of more than 1,000 Catholics by the Forsa Institute published by daily Bild, found 23 percent of Church members said they were thinking of leaving.
Even among those who described themselves as devout, 19 percent were considering walking away, the poll found.
The findings come as the Church faces its gravest crisis of modern times, with decades-old claims of child sexual abuse by priests surfacing in Germany and around the world. The scandal has this week forced the resignation of Augsburg Bishop Walter Mixa, who was accused of beating children at an orphanage, though not of sexual abuse.
At the heart of the anger is the belief that the Church is not handling the child abuse affair openly. Just 16 percent of Catholics polled said they believed Church leaders were dealing with the abuse crisis transparently, compared with 77 percent who said it was not transparent.
Just under a quarter (24 percent) of people thought child abuse was more common in the Church than it was elsewhere in the community, compared with 14 percent who felt it was less common and 52 percent who believed it was the same.
Exactly half believed there was a link between celibacy and child abuse, while 44 percent said there was no link.
Yet a massive 81 percent believed celibacy for priests should be abolished, compared with just 12 percent who believed it should be kept.
The disillusionment was felt most deeply by younger Catholics. Among those aged 18 to 29, just over a third (34 percent) were thinking of quitting. Some 28 percent of those aged 30 to 44 were considering walking away, as were 32 percent of 45 to 59-year-olds and 6 percent of those aged 60 or older.