I have to admit I was skunked until I looked this one up (came across it in the new Smithsonian).
The word is not listed in Cambridge or Merriam-Webster, and there's only 4 hits on OneLook, all pretty generic with no etymolgies. This is the best I could find, from YourDictionary.com:

mustelid n : fissiped fur-bearing carnivorous mammals [syn: musteline mammal, musteline]

Any OED'ers, or anyone, whom I could badger for more background on this word? I'm assuming Latin. But since I left most of my Latin back in 9th grade with a one-year course, "Salve magistra!," I'll have to toss this one over to Faldage.