It can be turned off in FaceBook's settings.
In the app tap More > Settings > Account Settings > Videos and Photos then change AutoPlay to Never AutoPlay Videos or On Wi-Fi Connection only. Whichever you prefer.
You should be able to find the same setting on the FaceBook website; though I don't have the exact path handy. It might be necessary to change it both in the app and on the website (if you use both). I seem to remember turning it off on my computer, but noticed that it was still on in the app on the iPad.