It does, see Private Browsing on Firefox for Android and sorry it was not easier to find for you.

Let us know if this solves your question.

Is there any way of blocking or disabling private browsing mode on this browser?

Completely understandable. Off the top of my head I can't think of any browsers per se, but you can disable the private browsing mode in firefox

Go to your C: Drive and navigate to program files/Mozilla firefox/components

NOW, make sure you are searching for all files under 'files of type'.

Then, you will be able to see "nsPrivateBrowsingService.js"

Right click and DELETE!!!

This won't remove the controls but it will make it stop working. You may have to go in and disable again after an update.

see source if you would like to remove the option but it does get quite a bit technical

source:http://superuser.com/questions/189327/how-can-i-disable-private-browsing-incognito-mode-in-browser-x

Awesome! Thanks! Would it work the same on a phone ? or would it be a different process to block it on a phone?

That process would not work on Firefox for Android.

I don't know of a way to disable the feature on Firefox for Android.

Oh shoot... Ok thanks for your help. :)

If yo are looking for ways to prevent people from browsing to sites without your consent, install a content filter, there are multiple programs for Android. Any in-browser changes can easily be circumvented.