This is a function that's already built into iPhones, which let you limit whether an app can track you any time, only when you're using it or never.
Facebook uses your location information to target ads, show you nearby events and to identify where you're logging in from, and it stores a copy of your precise location data. You have to manually enable Location History for Facebook to track you in the first place, but you may have done this if you've ever used a feature like location tagging for photos.
I'll show you how to stop Facebook from using your location on Android even when you don't have the app open.
The update is still rolling out, so you might not see that notification yet. If you don't, you can still turn off full access to Facebook's ability to track your phone location, even while you're using the app.
To do that:
And, in case you're an iPhone user, you can already stop Facebook — or any other app — from tracking you on an iPhone.