Police spokeswoman Claudia Hallersleben said the incident happened early this morning at a bar in Bremen when a heated argument between the two turned into a fist fight.
After bystanders separated them one jumped forward again and bit off a one-centimeter-long piece of the other man's nose and then ran away.
The victim, a 24-year old from Nordenham in northern Germany who was not identified, had to be treated at a hospital.
Hallersleben said police are still looking for the attacker.