Upvote:4
If the student visa you already have is a uniform type D visa, then it allows you to make short visits to the other Schengen states.
I don't know whether leaving Italy is going to jeopardize any local Italian bureaucratic procedure that you've already started at that point, though. (And Expats would be a better place to ask that, anyway). I'd guess probably not -- the Italian authorities have little reason to even know that you go on a weekend trip to Germany.
But to play it safe, if you have 8 working days from your first arrival to file a local application, a possible strategy might be to file only after you get back from Munich.