Moving a Musical Instrument on Shabbat

Is it permissible to move a musical instrument on Shabbat to prevent it from being stolen or broken?

You didn’t specify which type of musical instrument you’re asking about. In principle, a musical instrument that is carefully preserved so as not to be used for anything else that might damage it, is considered 'muktzeh due to monetary loss’ (“muktze machmas chisron kis”), and it is forbidden to move it for any reason at all. A simple musical instrument that is not carefully preserved, and if necessary, can be used for some other purpose, for example, as a paperweight, or as an stick to help one reach and move something, is considered “a tool whose labor is forbidden” (“melachto le-isur”) and it is permissible to use it for a permitted type of labor. For example, one is allowed to remove something from a high shelf with the help of a flute. One is also allowed to move it when wanting to clear the space. However, it is forbidden to move it in order to protect it.

Shulchan Aruch (Orach Chaim, Chapter 308, Paragraphs 1-4).