Either can be correct depending on the context. I would say 'My brother is at university' if I was talking about him generally, maybe in answer to the question 'What does your brother do?' Which university isn't important.
It could also mean where he is physically right now 'He's not at home - he's at university' - we already know where the university is.
'the university' is more common if you are specifying university versus another place such as 'My brother lives in London. He's at the university there' or 'she's at the school on top of the hill'.
'At university' or 'at school' are both far more common so use those if you have any doubts.