This is not possible for a third-party app and a non-jailbroken device. Did you look at Settings → General → Restrictions? It’s not exactly what you’re after, but it’s a good start.
Actually, this is possible, using the Device Enrollment Program. (This YouTube video found by Kudi shows the device enrollment profile installation procedure.) The DEP is mostly meant for large companies managing their company devices, but apparently it can also be used for other features. It would be interesting to hear the details from somebody who has jumped through the hoops, I have no experience with DEP myself.
