Moby is Ed Grimley's fish who lives in his apartment with him in Muppets Tonight episode 110. When Grimley's great uncle Balfour dies and leaves him a fortune (all of $85 in Canadian exchange), he's forced into a quick marriage with his new neighbor, Miss Piggy. Since Moby is a sea captain, he's able to perform the marriage ceremony with a simple exchange with the involved parties. After the two are married and Piggy learns how much she has married into, she demands an annulment. To her dismay, the process will take about twenty minutes, for the paperwork is to be prepared under water.

Moby's name may be a reference to Herman Melville's novel Moby-Dick. In Martin Short's original Ed Grimley sketches on SCTV and Saturday Night Live, the role of Moby was often portrayed by a real goldfish.