Bishop Walter Mixa wrote a letter to the Pope offering to step down in the hope of allowing a "new start" for his diocese, the Augsburg diocese said in a statement.
He said he would co-operate fully with investigators and offered an apology.
"I ask the forgiveness of all those to whom I may have been unfair and to those whom I may have caused heartache," Bishop Mixa wrote, acknowledging that he was "fully aware of my own weaknesses".
Bishop Mixa has been accused of hitting children while a priest decades ago. He initially denied ever using violence against youngsters, but later acknowledged he may have slapped children.
Although the case does not involve any allegations of sexual abuse, Bishop Mixa has been a key member of Germany's Bishops' Conference for more than a decade and his initial denial of physical violence fuelled frustration among German Catholics that the Church appeared to be unwilling to come clean on the issue of abuse.
Adding to Bishop Mixa's troubles, a special investigator has found financial irregularities at a children's home under his responsibility around the same time as the allegations of abuse.
Bishop Mixa said in his letter he would support efforts for a "thorough investigation" into all the allegations.
On Wednesday, the head of the national Bishops' Conference had urged Bishop Mixa to take leave until the allegations are cleared up, German media reported.
Archbishop Robert Zollitsch said he had several phone conversations with Bishop Mixa in recent days to discuss "how to contribute to calming down the current difficult situation in the Augsburg diocese", according to the DDP news agency.
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