Even though it might sound incorrect, the best way to translate this sentence would be the last sentence:

Je dois aller en classe dans dix minutes.

Do note though that in France, we usually do not say that we go “en classe”, but “en cours”. So nearly all of the time, you will hear people say:

Je dois aller en cours dans dix minutes.

Your second (and first one too somehow) sentence would be translated as:

I have to go to the classroom in ten minutes.

The English “class” is usually translated into French by cours. So I would say :

Je dois aller en cours dans dix minutes.
Il faut que je sois en cours dans dix minutes.

If you actually mean the place, as some people use “class” for “classroom”, then you could say:

Il faut que je sois en classe dans dix minutes.
Je dois aller en classe dans dix minutes.

But note that classe would only be used by a student at secondary level and not at university level.