But the 53-year-old from the small town of Unterschleichach said he had not intended to hit Janina, who died in hospital after a bullet struck her head, Bild reports.
Roland E. said that after splitting from his family he had spent the New Year alone.
Out of anger at the noise outside he went into his cellar and picked up his gun before firing three or four shots into the crowd, he admitted to police.
A 50-man special investigation was set up after the tragic death, broadcaster Bayerische Rundfunk (BR) reports, with police finally making an arrest on Tuesday.
Roland E. is a court clerk and the owner of the small-caliber weapon from which the deadly shot was fired, investigators say.
A bullet hit the young girl in the head as she was watching a New Year's firework display with friends and she died a few hours later in hospital.
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While the girl's mother appealed for the killer to come forward in the days after the attack, no one admitted to the crime.
The special investigation team went through the local gun register and found Roland E.'s name among those who hold gun licences in the small town of Unterschleichach, where the killing took place.