There's a couple of questions you're asking.
Why the article and do you really need it? It's clear you are calling on a specific next something so it does make sense to have the definite article. Of course in an exclamation you don't have to be complete and 100% grammatically correct, so no, but 'Volgende!' could be seen as a command or as if you really don't care, just as 'Next, please!' might also be more appropriate in for example a shop.
Which definite article, 'de' or 'het'? 'next'/'volgende' is an adjective acting as a noun here so that doesn't really help. When it's not clear, 'de' and it's rules usually apply. We could have 'De volgende klant!', 'Volgende klant!', 'De volgende!', 'Volgende!'
What if we are specifically referring to a pile of books? 'Het volgende boek!', 'Een volgend boek!', 'Volgend(e) boek!', 'Het volgende!', 'Volgend(e)!'. I would personally hesitate dropping the '-e' since it is still definite and the 'het' is implied even if you don't say it. Also once you drop the 'boek' part and the adjective gets promoted to more of a noun, do you still have to follow the het-rules? On the other hand you do say 'Volgend jaar ga ik naar Spanje.' and an '-e' ending would be wrong here.