Upvote:2
Yes, you will have to re-apply and from Italy (or from Austria) instead of from Germany.
While Schengen visa are valid for the whole area in theory, in practice you have to make the travel you applied for. As you applied for a short visit to Germany, your changed plans are really different from the one you applied for.
The reason they do not allow this kind of change is that people would apply for a visa where it is 'easy' and then travel to a different country for which it is harder to get a visa. Which is very much against the rules.