Gail Zappa also wants the club to stop selling live concert recordings of her late husband's music or CDs and t-shirts with images of his distinctive facial hair.
The suit's aim is not to shut down the festival, Gail Zappa's lawyer said, but to protect the artistic quality of the music. Festival organizers could face fines of €250,000.
Fans first organized the festival in the eastern city of Bad Doberan in the German state of Mecklenburg-Western Pomerania 18 years ago, before Frank Zappa's death in 1993. Fan representatives argued at the Wednesday hearing, held in Düsseldorf, that the longstanding event has developed into its own brand.
A decision is expected within about three months.