Maria Jepsen stepped down saying her credibility had been contested.
She denies having known before May this year about a priest in the town of Ahrensburg who reportedly sexually abused boys and girls in the 1980s.
Several cases in Germany form part of sex abuse scandals that have hit the Roman Catholic Church recently.
Maria Jepsen was elected bishop in 1992, becoming the first woman worldwide to hold the post.
"My credibility has been put in question," she said.
"Consequently, I feel that I am no longer able to spread the good word, as I vowed to do at my ordination.
"I expect that the... cases in Ahrensburg and elsewhere will be swiftly investigated and that the truth will come to light."
Maria Jepsen is the third bishop to resign in Germany in recent months.
Roman Catholic Bishop Walter Mixa resigned in April after claims he hit children.
And the former head of the Protestant Church in Germany, Margot Kaesmann, resigned after she was caught by police drunk driving.
Speedy solutionIn recent months, allegations of abuse levelled against Catholic priests have surfaced in many countries.
There have also been accusations that Church authorities in Europe and North and South America failed to deal with cases openly or properly.
Pope Benedict XVI himself has been accused of being part of a culture of secrecy, and of not taking strong enough steps against abusers when he had that responsibility as a cardinal in Rome.
However, his supporters say he has been the most pro-active pope yet in confronting abuse.
The Pope pledged in April to "bring to justice" Church officials responsible for abuse.
On Thursday, the Vatican issued new instructions to speed up the handling of the "most urgent" cases of sex abuse by priests, after a series of abuse scandals.
Priests who sexually abuse a mentally ill adult will now be treated in the same way as those who abuse minors.
SIC: BBC