Fishman calls himself "the hugest Zappa fan in the world", and regarding Zappa's influence on other musical artists calls him "a musician's musician". He became a Zappa fan when he was 12 or 13 years old and was searching for the album with the song Cosmik Debris on it. He assumed the track could be found on Sheik Yerbouti and bought that album first. The song Bobby Brown Goes Down shocked his mother and she wanted to take the album away from him. Eventually Fishman found Apostrophe and his mother changed her mind when she saw Zappa performing I'm The Slime on Saturday Night Live, because she liked his criticism of television.
Fishman picked his favourite Zappa tracks for the homage compilation Zappa Picks By Jon Fishman Of Phish.
On Phish' album "Vegas '96" (2007) the band covered "Peaches En Regalia".