Is it possible to disable Personal Hotspot on iPhones with a configuration profile?

As of iOS 9.2, there is no way to disable the Personal Hotspot feature through Configuration Profiles.

The best you can do at the moment is to use an MDM server to report on the status of the Personal Hotspot feature and manually instruct users to switch it off, or arrange to disable it through your carrier.

Yes,you can.I just spoke with AT&T and they walk me through a process.I have IPHONE 6. You go to Settings#General#Restrictions,select ON#Data# select "Don't alow changes"

This is not quite what the OP is looking for because their question is coming from a business context, but for those who may be interested in this question for parental control related reasons: I think when Qustudio is set up using a VPN as instructed in the link below a side effect is that tethering is effectively disabled (you can still start tethering and connect devices but those connected devices will not have any internet access via the tethering).

https://www.qustodio.com/pt/help/article/2076783/ (Note: I think the use of a Supervised phone setup in the link may not be necessary, probably any way of setting Qustudio up on ios would work. Though this is probably the most robust setup)