From Muppet Wiki

The Wicked Witch of the East appears in The Muppets' Wizard of Oz. Along with her sisters Tattypoo, Glinda, and the Wicked Witch of the West, the Witch of the East was part of a successful singing group before they went their separate ways, and became the East Coast diva. In that capacity, she terrorized the Munchkins, and apparently in common with other fairytale witches, she enjoyed cooking her victims in her oven.

Her appearance in the film is a small but showy cameo, valiantly resisting the pressure of Dorothy Gale's double-wide trailer to snarl and insult the Munchkins one last time, before finally succumbing to the weight, and a rather messy death. Her magic slippers, and the fight for ownership of them, set off a chain reaction and affect the overall plot.