Shiny Wobbuffet Pokémon Go is available, but you'll need some patience to catch the Patient Pokémon.
Shiny Wobbuffet Pokémon Go: How to Catch
You might have encountered a Shiny Wobbuffet during the Spotlight Hours. If you missed the event, you can still try to find a Shiny Wobbuffet with traditional means.
Finding a Shiny is all down to luck, with about a 1/450 chance of finding a particular Pokémon's Shiny form. You won't see Shiny Pokémon on the map, you'll only know for certain when you get into the encounter for catching.
Shiny Wobbuffet is easy to notice: it's entirely purple instead of blue.
Unfortunately, Wobbuffet is almost stone useless as a Pokémon. It has one gimmick: it can't directly attack the enemy. Wobbuffet must counterattack, using the moves Mirror Coat and Counter in response to getting hit.
This makes Wobbuffet unusable in most applications, but it does defend Gyms really well. Stick up a Shiny Wobbuffet for style points.