I have a Samsung Galaxy SII and cannot get this to quit! It's not showing up in my downloads, when I try long clicking on it in my active applications it just brings me to my home page and I disabled FB (which is not showing anywhere on my phone but I'm unable to enable in Play Store). PLEASE HELP!
I'm getting it as well, along with a bunch of people who also posted this problem today on Android Central. To fix it, long press on the notification until "app info" pops up. Go into app info, force stop it, and then clear data.
Alternatively, find the app called "downloads" in your app drawer, open it, press the "other downloads" button on the right. You should see the Facebook download with an in progress status. Tick the box next to it and then press the little trashcan icon to delete it.
Problem solved.
Edit: Probably best to do both methods, as it came back on me once after just deleting it from downloads app.