In the US we typically say that classes are offered rather than given
The preposition will be by or at, not from.
What is offered is more likely to be courses than classes. Classes tends to be used more in secondary-school or non-academic contexts.
So:
English courses for people whose native language is not English are offered by that university.
But note: the passive is awkward in this instance. Other things being equal, English prefers to put “heavy” constituents—those with many words—at the end of a sentence rather than the beginning or middle, because the syntactic structure is most visible when the primary constituents are close together at the front. Compare the structures for the passive and active sentences:
[Subj English courses MinAdj for people whose native language is not English] [Verb are offered] [MajAdj by that university.]
[Subj That university] [Verb offers] [DirObj English courses MinAdj for people whose native language is not English.]
In the passive sentence, that's a long run from Subject to Verb. In this case you could get around this by moving the “minor” adjunct to the end:
English courses are offered by that university for people whose native language is not English.
[Subj English courses] [Verb are offered] [MajAdj by that university] [MinAdj for people whose native language is not English.]