I don't know that the Muppet Animal has a specific genus. Here is a broader description of Henson's creatures and their appearances:
A common design for a Jim Henson Muppet is a character with a very wide mouth and large protruding eyes. The puppets are often molded or carved out of foam rubber, and then covered with fleece. Muppets may represent humans, anthropomorphic animals, realistic animals, robots, extraterrestrial creatures, mythical beings or other unidentified, newly imagined creatures, monsters or abstract characters.
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