Bishop Walter Mixa's Augsburg diocese said last week it had referred the allegations to prosecutors but gave no details.
Ingolstadt prosecutor Helmut Walter said a preliminary investigation has been closed because "a crime could not be established."
Mixa's lawyer had rejected the accusations.
Mixa offered his resignation last month following separate allegations of physical abuse of children and financial misconduct.
Pope Benedict XVI accepted the resignation last weekend.
Mixa initially denied ever using violence against youngsters but later said he may have slapped children.
Later on Friday, an independent special investigator looking into the case released a report detailing the physical abuse allegations against Mixa.
In his report, Sebastian Knott wrote that Mixa hit children while serving as a priest decades ago, the German news agency DAPD reported.
Knott published victims' statements saying they had been brutally punched, hit with sticks and in one case even beaten with a belt.
Knott also confirmed financial irregularities at a children's home under Mixa's responsibility around the same time as the allegations of abuse.
SIC: AP