For mobile-data (LTE/etc) yes, you can go into the "Cellular" section in the settings and disable/enable using cellular data for any app.

On wifi, not that I'm aware of.

Out of curiosity, what do you mean they need permissions on Android? Up until the last Android version (Marshmallow), you either gave an app all permissions or didn't install it. To deny network traffic outside of that you basically had to have root access (which is functionally equivalent to jailbreaking).