The suspect had a license to own firearms as a shooting club member, Moeller said. Authorities believe he used a semi-automatic pistol.
"We can't say anything so far about the motive," he said. "Because of the victims and the wounded, we believe it was a family drama, since according to what we know at present all were related to each other."
The suspect's mother and father were among the dead, the police chief said. Police were working to clear up how the others were related.
They planned to question the suspect and were waiting for his lawyer.
Rot am See is located about 170km northwest of Munich. It is a town of some 5300 people in a rural area of Baden-Wuerttemberg state.
Private gun ownership is relatively high in Germany compared to some other countries in Europe, with about 20 firearms per 100 citizens. However, gun laws are stringent, and many people keep their weapons at ranges and gun clubs.
Gun laws were restricted after a gunman killed 16 people at a school in Erfurt in 2003, and again after another school shooting in 2009 which claimed 15 lives. Ownership of semiautomatic weapons is severely restricted. Gun owners must obtain a license. The suspect in Friday's shooting holds one, according to German news reports.
- AP, with Washington Post