From Muppet Wiki

The Green Fairy was found in Kermit's drink in the "Moulin Scrooge" number of It's a Very Merry Muppet Christmas Movie. Besides being a part of the musical "Moulin Rouge", the Green Fairy's inclusion in the number provides the set up for a joke by Fozzie Bear.

The character is a spoof of the Green Fairy (played by Kylie Minogue) in Moulin Rouge.